11.3 Graphing with intercepts  (Page 2/4)

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To find the x- intercept, let $y=0$ :

Substitute 0 for y .
Add.
Divide by 2.
The x -intercept is (3, 0).

To find the y- intercept, let $x=0$ :

Substitute 0 for x .
Multiply.
Add.
The y -intercept is (0, 6).

The intercepts are the points $(3,0)$ and $(0,6)$ as shown in the chart.

Solution

To find the $x\text{-intercept,}$ let $y=0.$

The $x\text{-intercept}$ is $(3,0).$

To find the $y\text{-intercept},$ let $x=0.$

The $y\text{-intercept}$ is $(0,\mathrm{-4}).$

The intercepts are the points $(\mathrm{-3},0)$ and $(0,\mathrm{-4}).$

Solution

First, find the $x\text{-intercept}.$ Let $y=0,$

$\begin{array}{}\\ -x+2y=6\\ -x+2(0)=6\\ -x=6\\ x=\mathrm{-6}\end{array}$

The $x\text{-intercept}$ is $(–6,0).$

Now find the $y\text{-intercept}.$ Let $x=0.$

$\begin{array}{}\\ -x+2y=6\\ \mathrm{-0}+2y=6\\ \\ \\ 2y=6\\ y=3\end{array}$

The $y\text{-intercept}$ is $(0,3).$

Find a third point. We’ll use $x=2,$

$\begin{array}{}\\ -x+2y=6\\ \mathrm{-2}+2y=6\\ \\ \\ 2y=8\\ y=4\end{array}$

A third solution to the equation is $(2,4).$

Summarize the three points in a table and then plot them on a graph.

Do the points line up? Yes, so draw line through the points.

Solution

Find the intercepts and a third point.

We list the points and show the graph.

Solution

This line has only one intercept! It is the point $(0,0).$

To ensure accuracy, we need to plot three points. Since the intercepts are the same point, we need two more points to graph the line. As always, we can choose any values for $x,$ so we’ll let $x$ be $1$ and $\mathrm{-1}.$

Organize the points in a table.

Plot the three points, check that they line up, and draw the line.