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PSLE

PSLE Foundation Mathematics

<p>The diagram shows the points $A(-7,\ 5)$ and $B(5,\ -4)$.</p>
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<p>Find</p>
<ol class="i-list"><li data-list-item-id="cg-q01-i" data-list-item-path="cg-q01-i"><div class="list-item-paragraph">the length of $AB$,<span class="inline-marks">[2]</span></div></li><li data-list-item-id="cg-q01-ii" data-list-item-path="cg-q01-ii"><div class="list-item-paragraph">the coordinates of the midpoint of $AB$,<span class="inline-marks">[1]</span></div></li><li data-list-item-id="cg-q01-iii" data-list-item-path="cg-q01-iii"><div class="list-item-paragraph">the gradient of $AB$,<span class="inline-marks">[1]</span></div></li><li data-list-item-id="cg-q01-iv" data-list-item-path="cg-q01-iv"><div class="list-item-paragraph">the equation of $AB$.<span class="inline-marks">[2]</span></div></li></ol>

The diagram shows the points $A(-7,\ 5)$ and $B(5,\ -4)$.

the coordinates of the midpoint of $AB$,

Length of a Line Segment

Gradient of a Straight Line

Equation of a Straight Line

Midpoint of a Line Segment

Length, midpoint, gradient and equation from two points

Coordinate Geometry

<p>The points $A(1,6)$, $B(4,16)$ and $C(7,p)$ are collinear. Find $p$.</p>

The points $A(1,6)$, $B(4,16)$ and $C(7,p)$ are collinear. Find $p$.

Sec 3/4 E Math T04-Q11 - Using collinearity to find an unknown coordinate

<p>A company charges $\$ y$ for&nbsp;$x$ units of electricity used.<br>The charge $\$ y$ can be represented by the function $y = ux + 20$, where&nbsp;$u$ is a constant. Some corresponding values of $x$ and $y$ are given in the table below.</p>
<div class="content-block content-block--table"><div class="table-container"><table style="table-layout: fixed; width: 600px;"><colgroup><col style="width: 100px;"><col style="width: 100px;"><col style="width: 100px;"><col style="width: 100px;"><col style="width: 100px;"><col style="width: 100px;"></colgroup><thead><tr><th style="text-align: center; --cell-justify: center">$x$</th><th style="text-align: center; --cell-justify: center">$0$</th><th style="text-align: center; --cell-justify: center">$100$</th><th style="text-align: center; --cell-justify: center">$200$</th><th style="text-align: center; --cell-justify: center">$300$</th><th style="text-align: center; --cell-justify: center">$400$</th></tr></thead><tbody><tr><td style="text-align: center; --cell-justify: center">$y$</td><td style="text-align: center; --cell-justify: center">$20$</td><td style="text-align: center; --cell-justify: center">$50$</td><td style="text-align: center; --cell-justify: center">$80$</td><td style="text-align: center; --cell-justify: center">$110$</td><td style="text-align: center; --cell-justify: center">$140$</td></tr></tbody></table></div></div>
<ol class="abc-list"><li data-list-item-id="item-a"><div class="list-item-paragraph">On the grid, draw the graph of $y = ux + 20$ for&nbsp;$0 \le x \le 400$.<span class="inline-marks">[2]</span></div></li><li data-list-item-id="item-b"><div class="list-item-paragraph">Find the total cost if a household uses $140$ units of electricity.<span class="inline-marks">[1]</span></div></li><li data-list-item-id="item-c"><div class="list-item-paragraph">What does the constant term, $20$, represent?<span class="inline-marks">[1]</span></div></li><li data-list-item-id="item-d"><div class="list-item-paragraph">Find the value of $u$.<span class="inline-marks">[2]</span></div></li><li data-list-item-id="item-e"><div class="list-item-paragraph">What does the gradient of the graph represent in this context?<span class="inline-marks">[1]</span></div></li></ol>

A company charges $\$ y$ for $x$ units of electricity used.
The charge $\$ y$ can be represented by the function $y = ux + 20$, where $u$ is a constant. Some corresponding values of $x$ and $y$ are given in the table below.

Plotting of Straight Line on Graph Paper

Linear Graphs in Real Life Problems

2023 ACSBR EM S1 EOY Q14

Linear Graphs and Its Applications

<p>The coordinates of $4$ points are $A(2, 10)$, $B(4, 2k)$, $C(k, 28)$, $D(3k, 9k + 4)$. Find the value(s) of $k$ if</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">the points $A$, $B$, $C$ are collinear,</span></div></li><li><div class="list-item-content"><span class="list-item-text">$AB$ is parallel to $CD$.</span></div></li></ol>

The coordinates of $4$ points are $A(2, 10)$, $B(4, 2k)$, $C(k, 28)$, $D(3k, 9k + 4)$. Find the value(s) of $k$ if

the points $A$, $B$, $C$ are collinear,

Parallel and Perpendicular Lines

<p>Given that the first $5$ terms of a sequence, $T_n$, are $-2, 2, 6, 10, 14, \dots$, where&nbsp;$n = 1, 2, 3, 4$ and $5$.</p>
<ol class="i-list"><li data-list-item-id="item-i" data-list-item-path="item-i"><div class="list-item-paragraph">Find a formula for the $n^{th}$ term of the sequence, $T_n$, in terms of $n$.<br>Hence find $T_0$. (Hint: substitute $n = 0$ into the formula of the general term of $T_n$.)</div></li><li data-list-item-id="item-ii" data-list-item-path="item-ii"><div class="list-item-paragraph">In the grid below, plot $T_n$ against $n$, i.e., draw the points of which the coordinates are in the form of $(n, T_n)$, where&nbsp;$n = 1, 2, 3, 4$ and $5$. Hence, draw a straight line that passes through these points.</div></li><li data-list-item-id="item-iii" data-list-item-path="item-iii"><div class="list-item-paragraph"><strong>Using your graph</strong>, find the gradient, $m$, and the $T_n$-intercept, $c$, of the straight line. Hence write down the equation of the straight line in the form of $T_n = mn + c$.</div></li><li data-list-item-id="item-iv" data-list-item-path="item-iv"><div class="list-item-paragraph">Based on your answers above, determine whether</div><ol class="abc-list"><li data-list-item-id="item-iva" data-list-item-path="item-iv/item-iva"><div class="list-item-paragraph">whether the point $\left( \frac{1}{2},-4 \right)$ lies on the graph of the straight line or not, and</div></li><li data-list-item-id="item-ivb" data-list-item-path="item-iv/item-ivb"><div class="list-item-paragraph">$-4$ is a term of the sequence $T_n$ or not. Explain your answers.</div></li></ol><div class="list-item-after-content" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1767611033034-otwyfyeja5.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc2MTEwMzMwMzQtb3R3eWZ5ZWphNS5wbmciLCJzY29wZSI6ImRvd25sb2FkIiwiaWF0IjoxNzkyNjk1ODE0LCJleHAiOjE3OTI2OTYxMTR9.nHsn7ea2H4PGBduJAAJuPQlCuDkEPrMQ7VZgBeESVNI" alt="After sub-items image" class="aligncenter custom-width" style="max-width: min(400px, 100%); height: auto;" /></div></li></ol>

Given that the first $5$ terms of a sequence, $T_n$, are $-2, 2, 6, 10, 14, \dots$, where $n = 1, 2, 3, 4$ and $5$.

**Using your graph**, find the gradient, $m$, and the $T_n$-intercept, $c$, of the straight line. Hence write down the equation of the straight line in the form of $T_n = mn + c$.

Based on your answers above, determine whether

General Term of a Sequence

Testing Sequence Membership

 Number Patterns

<p>The figure below shows the parallelogram $ABCD$ in the Cartesian plane.</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">Find the gradients of the straight lines $AB$, $CD$, $BC$ and $AD$.</span></div></li><li><div class="list-item-paragraph">Based on your answers in (i), write down ONE condition which guarantees that the two straight lines are parallel.</div><div class="content-block list-item-image" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1767605663092-rtv0qls8axd.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc2MDU2NjMwOTItcnR2MHFsczhheGQucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY5NTgxNCwiZXhwIjoxNzkyNjk2MTE0fQ.mG7pdoUroxMW0JRsKleJTEaAPm9WY7y1E012zndEAnc" alt="List item image" class="aligncenter custom-width" style="max-width: min(230px, 100%); height: auto;" /></div></li></ol>

The figure below shows the parallelogram $ABCD$ in the Cartesian plane.

Find the gradients of the straight lines $AB$, $CD$, $BC$ and $AD$.

Based on your answers in (i), write down ONE condition which guarantees that the two straight lines are parallel.

Gradient of Straight Line

<p>The figure below shows the parallelogram $ABCD$ in the Cartesian plane.</p>
<ol class="i-list"><li data-list-item-id="item-i" data-list-item-path="item-i"><div class="list-item-paragraph">Find the gradients of the straight lines $AB$, $CD$, $BC$ and $AD$.</div></li><li data-list-item-id="item-ii" data-list-item-path="item-ii"><div class="list-item-paragraph"><p>What can be said about the gradients found in part <strong>(i)</strong>?</p></div><div class="graph-block" 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data-width="504" data-height="504" style="width:504px;height:504px;max-width:100%;display:block;margin:0 auto;"></div></li></ol>

 Gradient of Straight Line

<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">On the grid below, draw the graphs of</span></div><ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">$y = -\frac{1}{2}x + 1$,</span></div></li><li><div class="list-item-content"><span class="list-item-text">$y = -\frac{1}{2}x - 2$,</span></div></li><li><div class="list-item-content"><span class="list-item-text">$y = -1$</span></div></li></ol></li><li><div class="list-item-content"><span class="list-item-text">Write down the gradients of the straight lines in (i).</span></div></li><li><div class="list-item-content"><span class="list-item-text">Based on your drawings in (i), identify the geometrical shape enclosed by the three graphs and $x$-axis.</span></div></li><li><div class="list-item-paragraph">Based on your answers in (ii) and (iii), write down ONE condition which guarantees that the two straight lines are parallel.</div><div class="content-block list-item-image" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1767605239734-ll2ofh2yesq.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc2MDUyMzk3MzQtbGwyb2ZoMnllc3EucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY5NTgxNCwiZXhwIjoxNzkyNjk2MTE0fQ.gFUU4q1ANWR7M41wTQUsYDseZRgSkkULMACch8MYSsM" alt="List item image" class="aligncenter custom-width" style="max-width: min(280px, 100%); height: auto;" /></div></li></ol>

Write down the gradients of the straight lines in (i).

Based on your drawings in (i), identify the geometrical shape enclosed by the three graphs and $x$-axis.

Based on your answers in (ii) and (iii), write down ONE condition which guarantees that the two straight lines are parallel.

<ol class="i-list"><li><div class="list-item-paragraph">On the grid below, draw the graph of</div><ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">$y = 4x - 3$,</span></div></li><li><div class="list-item-paragraph">$y = 4x + 8$</div><div class="list-item-paragraph">for value of $x$ from $-5$ to $5$.</div></li><li><div class="list-item-paragraph">$x=-1$</div></li><li><div class="list-item-paragraph">$x=1$</div><div class="list-item-paragraph">for value of $y$ from $-15$ to $15$.</div></li></ol></li><li><div class="list-item-content"><span class="list-item-text">Write down the gradients of the straight lines in (i).</span></div></li><li><div class="list-item-paragraph">Based on your drawings in (i), identify the geometrical shape enclosed by the four graphs.</div><div class="content-block list-item-image" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1767605045656-7jm00ulu9o.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc2MDUwNDU2NTYtN2ptMDB1bHU5by5wbmciLCJzY29wZSI6ImRvd25sb2FkIiwiaWF0IjoxNzkyNjk1ODE0LCJleHAiOjE3OTI2OTYxMTR9.AvcEdzkXlYRBjRiBCvSUbFl6JVZkH7HFoimoGui9Xgc" alt="List item image" class="aligncenter custom-width" style="max-width: min(280px, 100%); height: auto;" /></div></li></ol>

Based on your drawings in (i), identify the geometrical shape enclosed by the four graphs.

<p>The figure below shows $\Delta ABC$ in the Cartesian plane.</p>
<ol class="i-list"><li data-list-item-id="item-i" data-list-item-path="item-i"><div class="list-item-paragraph">On the same grid, mark and label the coordinates of $A$, $B$ and $C$.</div></li><li data-list-item-id="item-ii" data-list-item-path="item-ii"><div class="list-item-paragraph">Find the gradients of the straight lines $AB$, $BC$ and $AC$.</div></li><li data-list-item-id="item-1789466210432-35rhhnif6" data-list-item-path="item-1789466210432-35rhhnif6"><div class="list-item-paragraph"><p>In the same grid, draw the graph of $x = \frac{2}{5}$, for values of $y$ from $-1$ to $2$.</p></div><div class="graph-block" 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The figure below shows $\Delta ABC$ in the Cartesian plane.

On the same grid, mark and label the coordinates of $A$, $B$ and $C$.

Find the gradients of the straight lines $AB$, $BC$ and $AC$.

Basics of Coordinate Geometry

<p>A straight line passes through $A \ (0, \frac{8}{5})$ and $B\ (2, 0)$.</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">In the figure below, mark and label the points $A$ and $B$. Hence draw the line $AB$.</span></div></li><li><div class="list-item-paragraph">Find the gradient and $y$-intercept of the straight line $AB$.</div><div class="content-block list-item-image" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1767604178154-rk8kixbia6.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc2MDQxNzgxNTQtcms4a2l4YmlhNi5wbmciLCJzY29wZSI6ImRvd25sb2FkIiwiaWF0IjoxNzkyNjk1ODE0LCJleHAiOjE3OTI2OTYxMTR9.fqhk6JtAqUE6P5osPTqcpaf31z35L9udp33mfKxRLdg" alt="List item image" class="aligncenter custom-width" style="max-width: min(280px, 100%); height: auto;" /></div></li></ol>

A straight line passes through $A \ (0, \frac{8}{5})$ and $B\ (2, 0)$.

In the figure below, mark and label the points $A$ and $B$. Hence draw the line $AB$.

Find the gradient and $y$-intercept of the straight line $AB$.

<p>The figure below shows six line segments. Find the gradient of each of the line segments.</p>
<div class="content-block"><figure class="question-figure aligncenter" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1767603945683-yvhhguqyuh.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc2MDM5NDU2ODMteXZoaGd1cXl1aC5wbmciLCJzY29wZSI6ImRvd25sb2FkIiwiaWF0IjoxNzkyNjk1ODE0LCJleHAiOjE3OTI2OTYxMTR9.FFws6UHQVood4WIet-cmigwLQA0IgY_j8gMJ2YMra_4" style="max-width: min(290px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div>

The figure below shows six line segments. Find the gradient of each of the line segments.

<p>For each of the following straight lines, find the gradient and $y$-intercept.</p>
<ol class="i-list"><li><div class="content-block list-item-image" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1767603716120-ewz7m7zl287.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc2MDM3MTYxMjAtZXd6N203emwyODcucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY5NTgxNCwiZXhwIjoxNzkyNjk2MTE0fQ.kHNPfVrKP1go76294lQY_BZybBhCZDHTDRyaXvy3PXg" alt="List item image" class="aligncenter custom-width" style="max-width: min(220px, 100%); height: auto;" /></div></li><li><div class="content-block list-item-image" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1767603752501-qzolkimnlm.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc2MDM3NTI1MDEtcXpvbGtpbW5sbS5wbmciLCJzY29wZSI6ImRvd25sb2FkIiwiaWF0IjoxNzkyNjk1ODE0LCJleHAiOjE3OTI2OTYxMTR9.ej1zHRGaAcpCPnIcc_K7enIXnS3DMCaKf-VG8S7VJ2g" alt="List item image" class="aligncenter custom-width" style="max-width: min(220px, 100%); height: auto;" /></div></li><li><div class="content-block list-item-image" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1767603766300-yeyo5z4aet8.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc2MDM3NjYzMDAteWV5bzV6NGFldDgucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjY5NTgxNCwiZXhwIjoxNzkyNjk2MTE0fQ.bPUKrjm7kX9I3tu3KcspWOK5qOJCgVzciT2wxhr0fdQ" alt="List item image" class="aligncenter custom-width" style="max-width: min(200px, 100%); height: auto;" /></div></li><li><div class="content-block list-item-image" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1767603813628-qjatur2rik.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc2MDM4MTM2MjgtcWphdHVyMnJpay5wbmciLCJzY29wZSI6ImRvd25sb2FkIiwiaWF0IjoxNzkyNjk1ODE0LCJleHAiOjE3OTI2OTYxMTR9.H2Xy1dmsGq37tqnTNxibUzJ2ZgEklzwwHkHdMV3KNBA" alt="List item image" class="aligncenter custom-width" style="max-width: min(220px, 100%); height: auto;" /></div></li></ol>

For each of the following straight lines, find the gradient and $y$-intercept.

<p>Given a straight line $x+4y=36$, find</p>
<ol class="i-list"><li><div class="list-item-paragraph">the gradient of the line.</div></li><li><div class="list-item-paragraph">The point $\left( p,2p \right)$ lies on this straight line.  </div><div class="list-item-paragraph">Calculate the value of $p$.</div></li></ol>

<p>The equation of a straight line $AB$ is $\frac{x}{2}+\frac{y}{2}=1.$</p>
<ol class="i-list"><li><div class="list-item-paragraph">Find the gradient of line $AB$.</div></li><li><div class="list-item-paragraph">Find the $y$-intercept of line $AB$.</div></li><li><div class="list-item-paragraph">Another line $PQ$ is <strong>parallel</strong> to the line $AB$ and passes through a point $\left( 2,-8 \right)$.<br>Show that the second line $PQ$ also passes through the point $\left( -1,-5 \right)$.</div></li></ol>

The equation of a straight line $AB$ is $\frac{x}{2}+\frac{y}{2}=1.$

<p>The equation of a straight line is $3y+2x+6=0$. <br>Calculate</p>
<ol class="i-list"><li><div class="list-item-paragraph">the gradient of the line,</div></li><li><div class="list-item-paragraph">the equation of a line, <strong>parallel</strong> to the given line, that passes through the point $\left( 3,2 \right)$.</div></li></ol>

The equation of a straight line is $3y+2x+6=0$. 
Calculate

<p>$P$ is the point $\left( 0,11 \right)$ and $Q$ is the point $\left( 6,3 \right)$. <br>Calculate</p>
<ol class="i-list"><li><div class="list-item-paragraph">the gradient of the line $PQ$,</div></li><li><div class="list-item-paragraph">the equation of the line $PQ$,</div></li><li><div class="list-item-paragraph">the equation of the line <strong>parallel</strong> to $y-4x=7$ passing through $P$.</div></li></ol>

$P$ is the point $\left( 0,11 \right)$ and $Q$ is the point $\left( 6,3 \right)$. 
Calculate

<p>For each of the following equations, write down the gradient and the $y$-intercept of the line.</p>
<ol class="i-list"><li><div class="list-item-paragraph">$3x-6y+14=0$</div></li><li><div class="list-item-paragraph">$\frac{y}{2}+\frac{x}{3}=\frac{2}{5}$</div></li></ol>

For each of the following equations, write down the gradient and the $y$-intercept of the line.

<p>For each of the following equations, write down the gradient and the $y$-intercept of the line</p>
<ol class="i-list"><li><div class="list-item-paragraph">$5y=2x+6$</div></li><li><div class="list-item-paragraph">$\frac{y}{3}+\frac{x}{4}=-2$</div></li></ol>

For each of the following equations, write down the gradient and the $y$-intercept of the line

Finding gradient and $y$-intercept given its gradient

<p>The points $X,Y$and $Z$have coordinates $\left( 1,3 \right)$, $\left( -2,-3 \right)$ and $\left( 3,7 \right)$ respectively. Show that $X$, $Y$and $Z$ lies on a straight line.</p>

The points $X,Y$and $Z$have coordinates $\left( 1,3 \right)$, $\left( -2,-3 \right)$ and $\left( 3,7 \right)$ respectively. Show that $X$, $Y$and $Z$ lies on a straight line.

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