write an equation in slope - intercept form for the line described. write the slope and y - intercept as…

Explanation:

Step1: Find the slope of the required line

The slope - intercept form of a line is (y = mx + b), where (m) is the slope. For the line (y=-5x - 8), the slope (m_1=-5). If two lines are perpendicular, the product of their slopes is (- 1), i.e., (m_1\times m_2=-1). Let the slope of the required line be (m_2). Then (-5\times m_2=-1), so (m_2=\frac{1}{5}).

Step2: Use the point - slope form to find the equation of the line

The point - slope form of a line is (y - y_1=m(x - x_1)), where ((x_1,y_1)=(-2,2)) and (m = \frac{1}{5}). Substitute the values into the point - slope form: (y - 2=\frac{1}{5}(x + 2)).

Step3: Convert the point - slope form to the slope - intercept form

Expand the right - hand side: (y-2=\frac{1}{5}x+\frac{2}{5}). Add (2) to both sides. Since (2=\frac{10}{5}), we have (y=\frac{1}{5}x+\frac{2 + 10}{5}).

Answer:

(y=\frac{1}{5}x+\frac{12}{5})