Answer:
[tex]\large\boxed{y=-\dfrac{3}{10}x+\dfrac{1}{2}}[/tex]
Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points from the graph (-5, 2) and (5, -1).
Substitute:
[tex]m=\dfrac{-1-2}{5-(-5)}=\dfrac{-3}{10}=-\dfrac{3}{10}[/tex]
We have the equation in form:
[tex]y=-\dfrac{3}{10}x+b[/tex]
Put the coordinates of the point (5, -1) to the equation:
[tex]-1=-\dfrac{3}{10}(5)+b[/tex]
[tex]-1=-\dfrac{3}{2}+b[/tex]
[tex]-\dfrac{2}{2}=-\dfrac{3}{2}+b[/tex] add 3/2 to both sides
[tex]\dfrac{1}{2}=b\to b=\dfrac{1}{2}[/tex]
