How to Calculate Intercepts
In geometry, calculating x- and y-intercepts can help students quickly graph a line if it is in the slope-intercept form. The intercepts of a graph are the points at which the graph will cross the x-axis or the y-axis. The x- intercept has a y-coordinate of zero, while the y-intercept will also have an x-coordinate that is zero. To graph a line, you will make some simple substitutions to calculate the x-intercept and the y-intercepts.
Other People Are Reading
Instructions
-
-
1
Understand that the equation of a line is y= mx+b and has a slope of "m" and a y-intercept of "b." Any equation written this way is in the slope- intercept form. Calculate x-intercept by setting y= 0 in the line equation and similarly locate the y-intercept by setting x=0 in this equation. Once you have these two points, the line can be graphed.
-
2
Learn to calculate x-intercept and y-intercept by using the line equation 2x+3y=12.
-
-
3
Write the equation in Step 2 in the slope-intercept form by first subtracting 2x from both sides of the equation and get 3y= -2x+12.
-
4
Using the equation in Step 3, divide both sides of the equation by 3. The equation y= (-2/3) x +4 is now in slope-intercept form.
-
5
Substitute x=0 into the equation in Step 4 to locate the y-intercept. The equation then becomes y= (-2/3) (0) +4 =4. The y-intercept is found to be at (0, 4). Note that you can calculate the y-intercept when given a line in the slope-intercept form by knowing that "b" in this equation is the y-intercept.
-
6
Locate the x-intercept by substituting y=0 into the equation in Step 4 to get 0= (-2/3) x +4. Subtracting 4 from both sides, the equation becomes -4= (-2/3) x. Multiply both sides of this new equation by -- (3/2) and solve for x, that is -4(-3/2) = 6=x. The x-intercept is located at the point (6, 0). Use the two points to graph the line.
-
1
Tips & Warnings
Note that for vertical lines x= C where C is a constant, there will not be a y-intercept. For lines y=C, the y-intercept is equal to the constant C.
