Question

use point - slope form to write the equation of a line that passes through the point (11, 18) with slope 3.

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 \((x_1,y_1)=(11,18)\) and the slope \(m = 3\).

Step3: Substitute values into the formula

Substitute \(x_1 = 11\), \(y_1=18\) and \(m = 3\) into the point - slope formula \(y - y_1=m(x - x_1)\).
We get \(y-18 = 3(x - 11)\).

Answer:

\(y - 18=3(x - 11)\) (If we want to convert it to slope - intercept form \(y=3x-33 + 18=3x - 15\), but the question asks for the equation in point - slope form, so the answer is \(y - 18 = 3(x - 11)\))