Question

Prealgebra- Find an equation of the line that passes through the given point and has the indicated slope m.

Answer 1

Given:

Slope, m = 1/3

Point: (x, y) ==> (-7, -3)

Let's find the equation of the line that passes through the point with the indicated slope.

Apply the slope-intercept form:

$y=mx+b$

Where:

m is the slope.

b is the y-intercept.

Plug in 1/3 for m, then input the coordinates of the point (-7, -3) for the values of x and y respectively, then solve for b.

We have:

$\begin{gathered} -3=\frac{1}{3}(-7)+b \\ \\ -3=-\frac{7}{3}+b \\ \\ b=-3+\frac{7}{3} \\ \\ b=\frac{3(-3)+1(7)}{3} \\ \\ b=\frac{-9+7}{2} \\ \\ b=-\frac{2}{3} \end{gathered}$

Therefore, the y-intercept of the line is:

b = -2/3

Hence, the equation of the line in slope-intercept form is:

$y=\frac{1}{3}x-\frac{2}{3}$

• ANSWER:

$y=\frac{1}{3}x-\frac{2}{3}$