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Linear Equations and Graphs

Intercepts

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

  • The x-intercept is the intersection of the line with the x-axis. As y = 0 everywhere along the x-axis, the x-intercept is obtained by putting y = 0 into the equation for the line.
  • The y-intercept is the intersection of the line with the y-axis. As x = 0 everywhere along the y-axis, the y-intercept is obtained by putting x = 0 into the equation for the line.

Example 3.

Find the x and y intercepts of the line y = 2x - 6:

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

0
=
2x - 6 (Add 6 to both sides)
6
=
2x (Divide both sides by 2)
3
=
x  

The x-intercept is 3.

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

y
=
2(0) - 6  
=
0 - 6  
=
-6  

The y-intercept is -6.

 

Study a few more examples by clicking "New Example" below. Before clicking on "y-intercept" or "x-intercept", see if you can find the same solutions.

Click on the buttons below for the x- and y-intercepts of

y = x +

 
x
y
0
0

 

 

 

 

Note that in general, by putting x = 0 into the equation y = mx + b we obtain y = b. Also, by putting y = 0 into y = mx + b and solving for x we get x = -b/m.

Hence, for the line y = m*x+b the y-intercept is b and the x-intercept is -b/m.

 

Experiment with the applet below, varying the value of b in the linear equation y = mx + b to see how changing the y-intercept b changes the graph. The initial graph shown is y = x + 0 or y = x. This has a y-intercept of zero and remains stationary for comparison.

Can't see the above java applet? Click here to see how to enable Java on your web browser. (This applet is based on free Java applets from JavaMath )

 

 

Exercise 3.

Now try to calculate the intercepts for a few example linear functions:

Compute the x- and y-intercepts of the equation

y = x +

 

x-intercept
y-intercept
 

 

 

Locating intercepts on a graph: Try exercise 3 again, this time using the "Intercept Applet" below. When opened the applet starts by illustrating the line f(x) = 2x - 4. You can replace this line by a line of your choice. Just type the equation for the line in the function box provided! Got that? Good. Now, to start this exercise first click on the "New Exercise" button above. Enter the equation of the line given into the Simple Graph applet. Use the zoom buttons to zoom in and out to locate the intercepts. Recall that the x-intercept is the point where the line crosses the x-axis and the y-intercept is the point where the line crosses the y-axis. Have you found these points? Good! Then check your answers above!

Can't see the above java applet? Click here to see how to enable Java on your web browser. (This applet is based on free Java applets from JavaMath )

<< The Graph of a Linear Function (Drawing a Graph Using 2 Points) | Linear Equations and Graphs Index | Slope (or Gradient) >>

 

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