Question

line equations from point/slope (point slope form)
question
use point - slope form to write the equation of a line that passes through the point (7, -16) with slope 3.

Explanation:

Step1: Recall Point - Slope Formula

The point - slope form of a line 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

We are given the point \((x_1,y_1)=(7, - 16)\) and the slope \(m = 3\).

Step3: Substitute Values into Formula

Substitute \(x_1 = 7\), \(y_1=-16\) and \(m = 3\) into the point - slope formula \(y - y_1=m(x - x_1)\).
We get \(y-(-16)=3(x - 7)\).
Simplify the left - hand side: \(y + 16=3(x - 7)\).

Answer:

\(y + 16=3(x - 7)\) (or if we expand it, \(y=3x-21 - 16=3x - 37\), but the point - slope form is \(y + 16=3(x - 7)\))