Coaching Centre
Gradient-intercept form y = mx + c
Reading the gradient and y-intercept from y = mx + c, writing the equation of a line, rearranging into gradient-intercept form and sketching lines.
The form
m changes the steepness; c slides the line up and down.
State the gradient and $y$-intercept of $y = 3x - 2$.
Find the equation of the line with gradient $4$ through $(1, 3)$.
Find the gradient of $2x + y = 6$.
Give $m$ and $c$ for $y = 3x - 2$, separated by a comma.
Read straight off.
Line with gradient $4$ through $(1, 3)$: $y = $ ?
$3 = 4 + c$.
Gradient of $2x + y = 6$?
$y = -2x + 6$.
Line with gradient $2$ and $y$-intercept $-5$: $y = $ ?
Substitute $m$ and $c$.
Line with gradient $-1$ through $(2, 5)$: $y = $ ?
$5 = -2 + c$, so $c = 7$.
Which line is parallel to $y = 3x + 1$?
Same gradient $3$.
Gradient of $x - 2y = 4$?
$2y = x - 4$, so $y = \tfrac{1}{2}x - 2$.
Line through $(0, 1)$ and $(2, 5)$: $y = $ ?
$m = 4 \div 2 = 2$, $c = 1$.
New numbers every time. Keep going until you get five in a row.