Use the given conditions to write an equation for the line in point-slope form and in slope-intercept form.

Passing through (-9,-6) and parallel to the line whose equation is y=-5x+5

Write an equation for the line in point-slope form.
y=-5 x-51

Step 1 ：First, we need to find the slope of the given line. The equation of the line is given in slope-intercept form, which is \(y = mx + b\), where \(m\) is the slope. So, the slope of the given line is \(-5\).

Step 2 ：Since the line we are trying to find is parallel to the given line, it will have the same slope. So, the slope of the line we are trying to find is also \(-5\).

Step 3 ：We are also given a point \((-9,-6)\) that the line passes through. We can use this point and the slope to write the equation of the line in point-slope form, which is \(y - y_1 = m(x - x_1)\), where \((x_1, y_1)\) is a point on the line and \(m\) is the slope.

Step 4 ：Substituting \((-9,-6)\) for \((x_1, y_1)\) and \(-5\) for \(m\) in the point-slope form gives \(y - (-6) = -5(x - (-9))\), which simplifies to \(y + 6 = -5(x + 9)\).

Step 5 ：To write the equation in slope-intercept form, we need to solve for \(y\). Doing so gives \(y = -5x - 45 - 6\), which simplifies to \(y = -5x - 51\).

Step 6 ：So, the equation of the line in point-slope form is \(y + 6 = -5(x + 9)\), and in slope-intercept form is \(\boxed{y = -5x - 51}\).