Question

use point-slope form to write the equation of a line that passes through the point (9, 15) with slope $-\frac{4}{3}$.

Explanation:

Step1: Recall point - slope formula

The point - slope form of a linear equation 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 point \((x_1,y_1)=(9,15)\) and the slope \(m =-\frac{4}{3}\).

Step3: Substitute values into formula

Substitute \(x_1 = 9\), \(y_1=15\) and \(m=-\frac{4}{3}\) into the point - slope formula \(y - y_1=m(x - x_1)\).
We get \(y - 15=-\frac{4}{3}(x - 9)\).

Answer:

\(y - 15=-\frac{4}{3}(x - 9)\)