Question

a line that includes the point (6, 7) has a slope of 2. 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 \((6,7)\), so \(x_1 = 6\) and \(y_1=7\). The slope \(m = 2\).

Step3: Substitute values into the formula

Substitute \(x_1 = 6\), \(y_1 = 7\) and \(m=2\) into the point - slope formula \(y - y_1=m(x - x_1)\). We get \(y - 7=2(x - 6)\).

Answer:

\(y - 7 = 2(x - 6)\)