Question

Write the equation of the line that passes through the points (0,4)and (-9, -3). Put your answer in fully reduced point-slope form,unless it is a vertical or horizontal line.

Answer 1

To determine the equation of the line you have to use the point-slope form

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

Where

(x₁, y₁) are the coordinates of one point on the line

m is the slope

We know two points crossed by the line (0, 4) and (-9,-3), using them we can calulate the slope as:

$m=\frac{y_1-y_2}{x_1-x_2}$

Where

(x₁, y₁) are the coordinates of one point on the line

(x₂, y₂) are the coordinates of a second point on the line

$\begin{gathered} m=\frac{4-(-3)}{0-(-9)} \\ m=\frac{4+3}{9} \\ m=\frac{7}{9} \end{gathered}$

Now that we know the slope of the line, we can determine the equation using

m=7/9 and (0,4)

$\begin{gathered} y-4=\frac{7}{9}(x-0) \\ y-4=\frac{7}{9}x \end{gathered}$

Pass "-4" to the other side of the equation to express the equation in slope-intercept form

$\begin{gathered} y-4+4=\frac{7}{9}+4 \\ y=\frac{7}{9}+4 \end{gathered}$