Question

a line passes through the point (1, -8) and has a slope of 9. write an equation in point-slope form for this line.

Explanation:

Step1: Recall point - slope formula

The point - slope form of a line is given by \(y - y_1=m(x - x_1)\), where \((x_1,y_1)\) is a point on the line and \(m\) is the slope of the line.

Step2: Identify values of \(x_1\), \(y_1\) and \(m\)

We are given that the line passes through the point \((1,-8)\), so \(x_1 = 1\) and \(y_1=-8\). The slope \(m = 9\).

Step3: Substitute values into the formula

Substitute \(x_1 = 1\), \(y_1=-8\) and \(m = 9\) into the point - slope formula \(y - y_1=m(x - x_1)\). We get \(y-(-8)=9(x - 1)\), which simplifies to \(y + 8=9(x - 1)\).

Answer:

\(y + 8=9(x - 1)\)