line c has an equation of ( y=\frac{4}{3}x + 9 ). line d is parallel to line c and passes through ( (-4,-4)…

Explanation:

Step1: Determine the slope of line d

Since line d is parallel to line ( y=\frac{4}{3}x + 9), their slopes are equal. The slope (m) of line d is (\frac{4}{3}).

Step2: Use the point - slope form

The point - slope form is (y - y_1=m(x - x_1)). Substitute (m=\frac{4}{3}), (x_1=-4), and (y_1 = - 4) into the formula: (y-(-4)=\frac{4}{3}(x-(-4))) (y + 4=\frac{4}{3}(x + 4))

Step3: Convert to slope - intercept form

Expand the right side: (y+4=\frac{4}{3}x+\frac{16}{3}) Subtract 4 from both sides: (y=\frac{4}{3}x+\frac{16}{3}-4) Since (4=\frac{12}{3}), then (y=\frac{4}{3}x+\frac{16 - 12}{3}) (y=\frac{4}{3}x+\frac{4}{3})

Answer:

(y=\frac{4}{3}x+\frac{4}{3})