Question

there is a line that includes the point (-8, 3) and has a slope of -7. 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 \((- 8,3)\), so \(x_1=-8\) and \(y_1 = 3\). The slope \(m=-7\).

Step3: Substitute values into the formula

Substitute \(x_1=-8\), \(y_1 = 3\) and \(m = - 7\) into the point - slope formula \(y - y_1=m(x - x_1)\).
We get \(y-3=-7(x - (-8))\), which simplifies to \(y - 3=-7(x + 8)\).

Answer:

\(y - 3=-7(x + 8)\)