Question

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 the formula

Substitute \(x_1=-18\), \(y_1 = 2\) and \(m = 1\) into the point - slope formula \(y - y_1=m(x - x_1)\). We get \(y-2 = 1\times(x-(-18))\), which simplifies to \(y - 2=x + 18\). If we want to write it in the more standard point - slope form (without simplifying the \(x\) - term), we can leave it as \(y - 2=1(x + 18)\) or just \(y - 2=(x + 18)\) since the slope of 1 can be omitted in the multiplication.

Answer:

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