Problem
Use the given conditions to write an equation for the line in point-slope form and in slope-intercept form. Passing through $(-5,-2)$ and parallel to the line whose equation is $y=-5 x+5$ Write an equation for the line in point-slope form. (Simplify your answer. Use integers or fractions for any numbers in the equation.)
Solution
Step 1 ：Given a point $(-5, -2)$ and a line parallel to $y = -5x + 5$
Step 2 ：Since parallel lines have the same slope, the slope of the required line is $-5$
Step 3 ：Use the point-slope form of a line: $y - y_1 = m(x - x_1)$
Step 4 ：Substitute the given point $(-5, -2)$ and slope $-5$ into the equation: $y - (-2) = -5(x - (-5))$
Step 5 ：\(\boxed{y + 2 = -5(x + 5)}\)
