Question

a line that includes the point (1, 1) has a slope of -5. 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 that the point \((x_1,y_1)=(1,1)\) and the slope \(m=- 5\).

Step3: Substitute values into the formula

Substitute \(x_1 = 1\), \(y_1=1\) and \(m=-5\) into the point - slope formula \(y - y_1=m(x - x_1)\).
We get \(y - 1=-5(x - 1)\).

Answer:

\(y - 1=-5(x - 1)\)