Answer:
D
Step-by-step explanation:
The point slope form of a line is [tex](y-y_1)=m(x-x_1)[/tex] where [tex]x_1=-2\\y_1=5[/tex]. We write
[tex](y-5)=m(x--2)\\(y-5)=m(x+2)[/tex]
Since the line is parallel to the line shown it will have the same slope. To find m, count the slope from each marked point on the graph. Count the rise then the run and create a fraction rise/run. The slope is -3/2. Now substitute it for m.
[tex](y-5)=-\frac{3}{2}(x+2)[/tex]
Convert to slope intercept form by simplifying.
[tex]y-5=-\frac{3}{2}x -\frac{6}{2} \\y=-\frac{3}{2}x -\frac{6}{2} +5\\y = -\frac{3}{2}x +\frac{4}{2}\\y=-\frac{3}{2} +2[/tex]
