Question

What is the equation of like that has a slope of -3/4 and goes through the point (8,-2)

Answer 1

The form of the linear equation is

$y=mx+b$

m is the slope

b is the y-intercept

Since the slope of the line is -3/4, then

$m=-\frac{3}{4}$

Substitute it in the form of the equation

$y=-\frac{3}{4}x+b$

To find b substitute x and y by the coordinates of a point on the line

Since the line passes through the point (8, -2), then

Substitute x by 8 and y by -2 in the equation to find b

$\begin{gathered} -2=-\frac{3}{4}(8)+b \\ -2=-6+b \end{gathered}$

Add 6 to each side

$\begin{gathered} -2+6=-6+6+b \\ 4=b \end{gathered}$

The equation of the line is

$y=-\frac{3}{4}x+4$