Question

A line passes through the point (-9,5) and has a slope of12 / 2Write an equation in slope-intercept form for this line.

Answer 1

The form of the slope-intercept of the linear equation is

$y=mx+b$

m is the slope

b is the y-intercept

Since the slope of the line is 2/3, then

$m=\frac{2}{3}$

Substitute it in the form of the equation

$y=\frac{2}{3}x+b$

Since the line passes through the point (-9, 5), then

Substitute x in the equation by -9 and y by 5 to find the value of b

$\begin{gathered} 5=\frac{2}{3}(-9)+b \\ 5=-\frac{18}{3}+b \\ 5=-6+b \end{gathered}$

Add 6 to both sides

$\begin{gathered} 5+6=-6+6+b \\ 11=b \end{gathered}$

Then the equation of the line is

$y=\frac{2}{3}x+11$