Chapter 15, Problem 2CR

a.

To determine

To find: the x -intercept of the graph of the given equation.

Answer to Problem 2CR

  $x=6$ .

Explanation of Solution

Given:

The given graph equation is $2x+3y=12$ .

Calculation:

As the given graph equation is $2x+3y=12$ .

Now, substitutes $y=0$ to find the x -intercept. Then,

  $\begin{array}{l}2x+3y=12\\ 2x+3\left(0\right)=12\text{{given equation}}\\ 2x=12\text{{}\because y=0\text{}}\\ x=\frac{12}{2}=6\text{{divide both sides by 2}}\end{array}$

Therefore, the x -intercept of the graph of the given equation is $x=6$ .

b.

To determine

To find: the graph of the slope of the given equation.

Answer to Problem 2CR

  $m=\frac{-2}{3}$ .

Explanation of Solution

Given:

The given graph equation is $2x+3y=12$ .

Calculation:

As the given graph equation is $2x+3y=12$ .

Now, to find the slope of the graph.

  $\begin{array}{l}2x+3y=12\left\{\text{given}\right\}\\ 3y=12-2x\left\{\text{subtract}\right\}\\ y=\frac{12-2x}{3}\left\{\text{divide}\right\}\\ y=\frac{-2x}{3}+4\\ y=mx+c\left\{\text{equation of the line}\right\}\\ \therefore m=\frac{-2}{3}\end{array}$

Hence, the graph of the slope of the given equation is $m=\frac{-2}{3}$ .

c.

To determine

To check: the given points is lie on the graph.

Answer to Problem 2CR

No.

Explanation of Solution

Given:

The given points is $\left(37,-21\right)$ .

Calculation:

As the given graph equation is $2x+3y=12$ .

Now, substitutes the given points in the above equation.

  $\begin{array}{l}2x+3y=12\left\{\text{given}\right\}\\ 2\left(37\right)+3\left(-21\right)=12\left\{\text{subtract}\right\}\\ 74-63=12\left\{\text{simplify}\right\}\\ 11\ne 12\end{array}$

Hence, the given points do not lie on the graph.