Chapter 9.2, Problem

To determine

Write an equation in point − slope form for the line passes through the point $(x_1,y_1)=(-3,6),$ with a slope $m=-7$ .

Answer

The equation is: $y-6=-7x-21$

Explanation of Solution

Given:

Write an equation in point − slope form for the line passes through the point $(x_1,y_1)=(-3,6),$ with a slope $m=-7$ .

Concept Used:

The slope of a line in the plane containing the x and y axes is generally represented by the letter m, and is defined as the change in the y coordinate divided by the corresponding change in the x coordinate, between two distinct points on the line.

Calculation:

Point − slope form of equation: $y-y_1=m(x-x_1)$

Given: $(x_1,y_1)=(-3,6),m=-7$

  $\begin{array}{l}y-y_1=m(x-x_1)\\ y-6=-7(x--3)\\ y-6=-7(x+3)\\ y-6=-7x-21\end{array}$

Thus, the equation is: $y-6=-7x-21$