Question

Write an equation of the line that is parallel to the given line and passes through the given point. $$y=-9 x-8,(7,-2)$$

Short answer

The equation of the line is \(y = -9x + 61\).

Step-by-step solution

Identify the slope of the given line

From the equation \(y=-9x -8\), it can be seen that the slope (m) of the given line is -9.

Use the point-slope form of the line equation

Substitute the slope (-9) and the given point \((7,-2)\) into the point-slope form \(y - y_{1} = m(x - x_{1})\). This gives \(y - (-2) = -9(x - 7)\).

Simplify the equation

Simplify the equation gained from step 2: \(y + 2 = -9x + 63\), which can be further simplified to \(y = -9x + 61\) by subtracting 2 from both sides of the equation. This is the equation of the required line.