Question

What is the equation of a line in point-slope form that has aslope of 4 and goes through the point (-8, 12)?

Answer 1

Given the slope and a point below;

$\begin{gathered} m=4 \\ (-8,12)\Rightarrow x_1=-8,y_1=12 \end{gathered}$

By using the point-slope equation formula as described below

$y-y_1=m(x-x_1)$

We can obtain the equation of the line with the above formula, we will have to substitute for y1, x1 and m. This process is shown below;

$\begin{gathered} y-12=4(x-(-8)) \\ y-12=4(x+8) \end{gathered}$

By using distributive property, we can remove the bracket and simplify to obtain the equation

$\begin{gathered} y-12=4(x)+4(8) \\ y-12=4x+32 \\ y=4x+32+12 \\ y=4x+44 \end{gathered}$

Hence, the equation of the line with slope of 4 and passing through the point (-8 , 12) is y = 4x + 44