Answer :
Given the points:
(x1, y1) ==> (-50, 18)
(x2, y2) ==> (40, -9)
Take the slope-intercept form:
y = mx + b
Where m is the slope and b is the y-intercept
To write the slope intercept form of the equation, find the slope.
Use the slope formula below:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]Thus, we have:
[tex]\begin{gathered} m=\frac{-9-18}{40-(-50)}=\frac{-9-18}{40+50}=\frac{-27}{90}=-\frac{3}{10} \\ \\ m=-\frac{3}{10} \end{gathered}[/tex]Substitute m for -3/10 in y = mx + b
[tex]y=-\frac{3}{10}x+b[/tex]To find the y-intercept, b, use the point (-50, 18).
Substitute -50 for x and 18 for y:
[tex]\begin{gathered} 18=-\frac{3}{10}\ast(-50)+b \\ \\ 18=-3(-5)+b \\ \\ 18=15+b \\ \\ \text{Subtract 15 from both sides:} \\ 18-15=15-15+b \\ \\ 3=b \\ \\ b=3 \end{gathered}[/tex]The y-intercept of the equation is 3.
Therefore, the slope intercept form of the equation is:
[tex]y=-\frac{3}{10}x+3[/tex]ANSWER:
[tex]y=-\frac{3}{10}x+3[/tex]