## Intercepts

There are two particular points on a line the are much easier to locate than most; namely, the intersection that the line with the *x*-axis and the *y*-axis.

You are watching: Graph y=2x+6

The

*is the intersection of the line with the*

**x-intercept***x*-axis. As

*y*= 0 all over along the

*x*-axis, the

*x*-intercept is obtained by placing

*y*= 0 into the equation because that the line.

The

*is the intersection the the line with the*

**y-intercept***y*-axis. As

*x*= 0 all over along the

*y*-axis, the

*y*-intercept is derived by placing

*x*= 0 into the equation because that the line.

### Example 3.

Find the *x* and *y* intercepts the the heat *y* = 2*x* - 6:

**x****-intercept:** placed *y* = 0 in the equation *y* = 2*x* - 6 and solve for *x*.

-6 |

The *y*-intercept is -6.

Study a couple of more instances by clicking "New Example" below. Before clicking top top "*y*-intercept" or "*x*-intercept", check out if girlfriend can uncover the very same solutions.

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Note the in general, by placing *x* = 0 into the equation *y* = *mx* + *b* we achieve *y* = *b*. Also, by putting *y* = 0 into *y* = *mx* + *b* and also solving because that *x* we obtain *x* = -*b*/*m*.

Experiment with the applet below, varying the worth of *b* in the direct equation *y* = *mx* + *b* to watch how changing the *y*-intercept *b* changes the graph. The early stage graph shown is *y* = *x* + 0 or *y* = *x*. This has a *y*-intercept that zero and also remains stationary for comparison.

**Can"t view the over java applet? **Click right here to see exactly how to enable Java on your internet browser. (*This applet is based on complimentary Java applets from* JavaMath )

**Locating intercepts on a graph: **Try practice 3 again, this time utilizing the "Intercept Applet" below. As soon as opened the applet starts by portraying the line *f*(*x*) = 2*x* - 4. You deserve to replace this line by a line of her choice. Just kind the equation for the heat in the function box provided! got that? Good. Now, to begin this exercise very first click ~ above the "New Exercise" button above. Enter the equation the the line offered into the straightforward Graph applet. Use the zoom buttons come zoom in and also out to locate the intercepts. Recall that the *x*-intercept is the allude where the line the cross the *x*-axis and the *y*-intercept is the point where the line the cross the *y*-axis. Have you found these points? Good! Then check your answer above!

**Can"t watch the over java applet? **Click below to see just how to allow Java top top your web browser. (*This applet is based on cost-free Java applets from* JavaMath )

The Graph the a Linear duty (Drawing a Graph using 2 Points) | linear Equations and Graphs table of contents | slope (or Gradient) >>

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