Chapter 1, Problem 3CR

(a)

To determine

To find:

An equation of a line using the following point and slope of the line:

  $\left(-3,5\right),m=-\frac{3}{2}$

Answer to Problem 3CR

An equation of a line is $y=-\frac{3}{2}x-\frac{1}{2}$ .

Explanation of Solution

Given information:

  $\begin{array}{l}\left(x_1,y_1\right)=\left(-3,5\right)\\ m=-\frac{3}{2}\end{array}$

Formula used:

An equation of a line passing through a point with slope is given by the following expression:

  $\left(y-y_1\right)=m\left(x-x_1\right)$

Calculation:

An equation of a line passing through a point $\left(-3,5\right)$ with slope $\left(m=-\frac{3}{2}\right)$ is given by the following expression:

  $\left(y-y_1\right)=m\left(x-x_1\right)$

Put the given data:

  $\begin{array}{l}\left(y-5\right)=-\frac{3}{2}\left(x-\left(-3\right)\right)\\ y-5=-\frac{3}{2}x-\frac{9}{2}\\ y=-\frac{3}{2}x-\frac{9}{2}+5\\ y=-\frac{3}{2}x-\frac{1}{2}\end{array}$

(b)

To determine

To find:

Three additional points through which the line passes.

Answer to Problem 3CR

Three additional points through which the line passes are $\left(-1.03,2.045\right),\left(0,0.5\right),\left(0.333,0\right)$ .

Explanation of Solution

Given information:

From sub-part (a):

The equation of line is $y=-\frac{3}{2}x-\frac{1}{2}$

Calculation:

An equation of a line passing through a point $\left(-3,5\right)$ with slope $\left(m=-\frac{3}{2}\right)$ is given by the following expression:

  $y=-\frac{3}{2}x-\frac{1}{2}$

The line equation is graphed as below:

  

From the graph:

Three additional points through which the line $\left(y=-\frac{3}{2}x-\frac{1}{2}\right)$ passes are

  $\left(-1.03,2.045\right),\left(0,0.5\right),\left(0.333,0\right)$ .