Chapter 13.2, Problem 2PSA

(a)

To determine

To rewrite: The equation $y-3x=1$ in y-form, find slope and y-intercept of the graph of the equation.

Answer to Problem 2PSA

The equation in y-form is $y=3x+1$ , slope and y-intercept of the graph of the equation $y=3x+7$ are $3$ , and $7$ respectively.

Explanation of Solution

Given:

The equations is $y-3x=1$ .

Calculation:

Rewrite the equation in y-form as follows.

  $\begin{array}{c}y-3x=1\\ y=3x+1\end{array}$

Compare the equation $y=3x+1$ with $y=mx+b$ .

  $\begin{array}{c}m=3\\ b=1\end{array}$

Therefore, the slope and y-intercept of the graph of the equation $y=3x+1$ are $3$ , and $1$ respectively.

(b)

To determine

To rewrite: The equation $y+5x=2$ in y-form, find slope and y-intercept of the graph of the equation.

Answer to Problem 2PSA

The equation in y-form is $y=-5x+2$ , slope and y-intercept of the graph of the equation $y=-5x+2$ are $-5$ , and $2$ respectively.

Explanation of Solution

Given:

The equations is $y+5x=2$ .

Calculation:

Rewrite the equation in y-form as follows.

  $\begin{array}{c}y+5x=2\\ y=-5x+2\end{array}$

Compare the equation $y=-5x+2$ with $y=mx+b$ .

  $\begin{array}{c}m=-5\\ b=2\end{array}$

Therefore, the slope and y-intercept of the graph of the equation $y=-5x+2$ are $-5$ , and $2$ respectively.

(c)

To determine

To rewrite: The equation $2x+3y=6$ in y-form, find slope and y-intercept of the graph of the equation.

Answer to Problem 2PSA

The equation in y-form is $y=-\frac{2}{3}x+2$ , slope and y-intercept of the graph of the equation $y=-\frac{2}{3}x+2$ are $-\frac{2}{3}$ , and $2$ respectively.

Explanation of Solution

Given:

The equations is $2x+3y=6$ .

Calculation:

Rewrite the equation in y-form as follows.

  $\begin{array}{c}2x+3y=6\\ 3y=-2x+6\\ y=-\frac{2}{3}x+2\end{array}$

Compare the equation $y=-\frac{2}{3}x+2$ with $y=mx+b$ .

  $\begin{array}{c}m=-\frac{2}{3}\\ b=2\end{array}$

Therefore, the slope and y-intercept of the graph of the equation $y=-\frac{2}{3}x+2$ are $-\frac{2}{3}$ , and $2$ respectively.

(d)

To determine

To rewrite: The equation $7-\left(6-2x\right)=4y$ in y-form, find slope and y-intercept of the graph of the equation.

Answer to Problem 2PSA

The equation in y-form is $y=\frac{1}{2}x+\frac{1}{4}$ , slope and y-intercept of the graph of the equation $y=\frac{1}{2}x+\frac{1}{4}$ are $\frac{1}{2}$ , and $\frac{1}{4}$ respectively.

Explanation of Solution

Given:

The equations is $7-\left(6-2x\right)=4y$ .

Calculation:

Rewrite the equation in y-form as follows.

  $\begin{array}{c}7-\left(6-2x\right)=4y\\ 4y=7-6+2x\\ 4y=2x+1\\ y=\frac{1}{2}x+\frac{1}{4}\end{array}$

Compare the equation $y=\frac{1}{2}x+\frac{1}{4}$ with $y=mx+b$ .

  $\begin{array}{c}m=\frac{1}{2}\\ b=\frac{1}{4}\end{array}$

Therefore, the slope and y-intercept of the graph of the equation $y=\frac{1}{2}x+\frac{1}{4}$ are $\frac{1}{2}$ , and $\frac{1}{4}$ respectively.