Question

use point - slope form to write the equation of a line that passes through the point (13, 5) with slope 1.

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 \((13,5)\), so \(x_1 = 13\) and \(y_1=5\). The slope \(m = 1\).

Step3: Substitute values into the formula

Substitute \(x_1 = 13\), \(y_1 = 5\) and \(m=1\) into \(y - y_1=m(x - x_1)\). We get \(y - 5=1\times(x - 13)\), which simplifies to \(y - 5=x - 13\).

Answer:

\(y - 5=x - 13\) (or in the more standard point - slope form \(y - 5 = 1(x - 13)\))