Question

use point-slope form to write the equation of a line that passes through the point (-18, 2) 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 \((- 18,2)\), so \(x_1=-18\) and \(y_1 = 2\). The slope \(m = 1\).

Step3: Substitute values into point - slope formula

Substitute \(x_1=-18\), \(y_1 = 2\) and \(m = 1\) into the formula \(y - y_1=m(x - x_1)\). We get \(y-2 = 1\times(x - (-18))\), which simplifies to \(y - 2=(x + 18)\) or \(y-2=x + 18\).

Answer:

The equation of the line in point - slope form is \(y - 2=x+18\) (or \(y - 2 = 1\times(x + 18)\))