Question

QuestionFind the equation of a line that contains the points (-5,2) and (4,6). Write the equation in slope-intercept form, usingfractions when required.

Answer 1

First, we have to find the slope using the following formula.

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

Where,

$\begin{gathered} x_1=-5 \\ x_2=4 \\ y_1=2 \\ y_2=6 \end{gathered}$

Let's use the coordinates above to find the slope.

$m=\frac{6-2}{4-(-5)}=\frac{4}{4+5}=\frac{4}{9}$

Now, let's use the point-slope formula to find the equation of the line.

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

Where,

$\begin{gathered} m=\frac{4}{9} \\ x_1=-5 \\ y_1=2 \end{gathered}$$\begin{gathered} y-2=\frac{4}{9}(x-(-5)) \\ y-2=\frac{4}{9}(x+5) \\ y-2=\frac{4}{9}x+\frac{20}{9} \\ y=\frac{4}{9}x+\frac{20}{9}+2 \\ y=\frac{4}{9}x+\frac{38}{9} \end{gathered}$

Therefore, the equation in slope-intercept form is y = 4/9x + 38/9.