Answer:
[tex]\large\boxed{D.\ y=-\dfrac{1}{5}x+\dfrac{32}{5}}[/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
We have the slope m = -1/5. Substitute:
[tex]y=-\dfrac{1}{5}x+b[/tex]
Put the coordinates of the given point (-3, 7) to the equation:
[tex]7=-\dfrac{1}{5}(-3)+b[/tex]
[tex]7=\dfrac{3}{5}+b[/tex] subtract 3/5 from both sides
[tex]6\dfrac{2}{5}=b\to b=\dfrac{6\cdot5+2}{5}=\dfrac{32}{5}[/tex]
