Equation of a Straight Line
Equation of a Straight Line
TGM Original
y=mx+c 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. **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 Examples **Given** | **Method** | **Example** Gradient and one point | y-y_1=m(x-x_1) | m=2 through (3,-1) y+1=2(x-3) y=2x-7 Two points | Find m first, then use the point-gradient form with either point. | (1,2) and (4,11) m= 11-24-1=3 y-2=3(x-1) y=3x-1 Gradient and y-intercept | y=mx+c | m=- 12, c=4 y=- 12x+4
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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 \(m<0\).
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