Chapter 1.2, Problem 81E

(a)

To determine

To graph: The equation $y=3x-6$ using the graphing utility.

Graph:

Consider the provided equation:

$y=3x-6$

Now, make the graph of the provided equation using online graphing calculator.

The graph of the equation $y=3x-6$ is a straight line which is increasing.

(b)

To determine

The $x$ -intercept of the graph for the equation $y=3x-6$ using part (a).

The $x$ -intercept of the graph for the equation $y=3x-6$ is $\left(2,0\right)$.

Explanation:

Consider the equation,

$y=3x-6$

The $x$ -intercept of the graph of an equation in the standard form, $y=ax+b$ is the value of $x$ for which $y$ equals zero. It is the point where, the line of equation cuts the x-axis.

By observing the graph, the line cuts the $x$ -axis at $\left(2,0\right)$.

Hence, the $x$ -intercept of the graph of the equation $y=3x-6$ is $\left(2,0\right)$.

(c)

To determine

The explanation of how the $x$ -intercept is related to the solution of the equation $3x-6=0$.

The $x$ -intercept $\left(2,0\right)$ is the solution of the equation $3x-6=0$.

Explanation:

Consider the equation,

$3x-6=0$

The $x$ -intercept graph of an equation in the standard form is $y=ax+b$ is the value of $x$ for which, $y$ equals to zero.

The $x$ -intercept of the graph equation is $y=3x-6$ is $\left(2,0\right)$.

Putting $x=2$ in the equation,

$\begin{array}{c}3\left(2\right)-6=0\\ 6-6=0\\ 0=0\end{array}$

Since, the equation is equivalent,

Hence, the $x$ -intercept $\left(2,0\right)$ is the solution of the equation $3x-6=0$.