Question

Graph each equation using the x- and y-intercepts.

$y=3x-6$

Short answer

Graph by using the x and y intercepts is:

Step-by-step solution

Step 1. State the concept for plotting a straight-line using equation.

The x-intercepts are where the graph crosses the x-axis, and the y-intercepts are where the graph crosses the y-axis.

Then, algebraically,

• an x-intercept is a point on the graph where y is zero, and
• a y-intercept is a point on the graph where x is zero.

More specifically,

• an x-intercept is a point in the equation where the y-value is zero, and
• a y-intercept is a point in the equation where the x-value is zero.

Step 2. Calculate the x and y - intercepts.

To find the x -intercept, plug in $y=0$in the equation $y=3x-6$ and solve for x.

$$\begin{gathered} y=3x-6 \\ 0=3x-6[\text{Plug\hspace{0.17em}\hspace{0.17em}in\hspace{0.17em}\hspace{0.17em}}y=0] \\ 6=3x-6+6 \\ 6=3x \\ \frac{6}{3}=\frac{3x}{3} \\ 2=x \end{gathered}$$

Therefore, x- intercept is $x=2$.

Now to find the y-intercept, plug in $x=0$in the equation $y=3x-6$ and solve for y.

$$\begin{gathered} y=3x-6 \\ y=3\cdot 0-6[\text{Plug\hspace{0.17em}\hspace{0.17em}in\hspace{0.17em}\hspace{0.17em}}x=0] \\ =0-6 \\ =-6 \end{gathered}$$

Therefore, y-Intercept is $y=-6$.

Step 3. Plot the graph.

Graph the line$y=3x-6$ with x and y intercepts points are$\left(2,0\right)$ and $\left(0,-6\right)$.

Thus, x and y intercepts arewidth="53" height="20" role="math">0,−6 and width="51" height="20" role="math">y=−6.