Question

there is a line that includes the point (-3, 1) and has a slope of 9. what is its equation in point - slope form? use the specified point in your equation. write your answer using integers, proper fractions, and improper fractions. simplify all fractions.

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 the point \((- 3,1)\), so \(x_1=-3\) and \(y_1 = 1\). The slope \(m = 9\).

Step3: Substitute values into the formula

Substitute \(x_1=-3\), \(y_1 = 1\) and \(m = 9\) into the point - slope formula \(y - y_1=m(x - x_1)\).
We get \(y-1 = 9(x-(-3))\), which simplifies to \(y - 1=9(x + 3)\).

Answer:

\(y - 1=9(x + 3)\)