How do you write an equation of a line with Slope = 8, passing through (4, –1)?

May 21, 2015

We will aim to derive the equation of the line in the standard slope-intercept form $y = m x + c$, where $m$ is the slope and $c$ is the intercept.

You have already been given $m = 8$, so we just need to find $c$.

Subtracting $m x$ from both sides of the equation $y = m x + c$, we arrive at:

$c = y - m x$.

We know that one point that satifies this equation is $\left(4 , - 1\right)$ since the line passes through it. So we can substitute our known values $m = 8$, $x = 4$ and $y = - 1$ into this formula to get $c$:

$c = y - m x = - 1 - \left(8 \times 4\right) = - 1 - 32 = - 33$

So the equation of the line is $y = 8 x - 33$