Question

a line passes through the point (9, -7) and has a slope of \\(\frac{4}{3}\\). 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 \((9,-7)\), so \(x_1 = 9\) and \(y_1=-7\). The slope \(m=\frac{4}{3}\).

Step3: Substitute values into the formula

Substitute \(x_1 = 9\), \(y_1=-7\) and \(m = \frac{4}{3}\) into the point - slope formula \(y - y_1=m(x - x_1)\). We get \(y-(-7)=\frac{4}{3}(x - 9)\), which simplifies to \(y + 7=\frac{4}{3}(x - 9)\).

Answer:

\(y + 7=\frac{4}{3}(x - 9)\)