$y=mx+c\qquad y-y_1=m(x-x_1)$ $m$ is the gradient, $c$ the $y$-intercept and $(x_1,y_1)$ a

Question

$y=mx+c\qquad y-y_1=m(x-x_1)$ $m$ is the gradient, $c$ the $y$-intercept and $(x_1,y_1)$ a point on the line. FormEquationCondition Two-point$(y-y_1)(x_2-x_1)=(y_2-y_1)(x-x_1)$Two distinct points General$ax+by+c=0$$a,b$ not both zero Examples GivenMethodExample Gradient and one point Two points Gradient and $y$-intercept

Accepted Answer

$y=mx+c$, where $m$ is the gradient and $c$ is the $y$-intercept. Vertical lines $x=a$ have undefined gradient, horizontal lines $y=b$ have zero gradient, and non-vertical lines slope upwards for $m>0$ and downwards for $m<0$.

Form	Equation	Condition
Two-point	\((y-y_1)(x_2-x_1)=(y_2-y_1)(x-x_1)\)	Two distinct points
General	\(ax+by+c=0\)	\(a,b\) not both zero

Given	Method	Example
Gradient and one point
Two points
Gradient and \(y\)-intercept

Equation of a Straight Line

Equation of a Straight Line

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