How to Find & Graph Intercepts

By Grace Williams

The x-intercept and y-intercept of a graph are the points at which a line crosses the x or y axis. On a graph, the x-axis is the line running horizontally while the y-axis runs vertically. When dealing with the equation of a line, the x-intercept is where the y variable equals 0 to represent hitting the axis. Likewise, the y-intercept is where the x variable equals 0. The Slope Intercept Form can help solve linear equations. The formula is y = mx + b, where "x" and "y" represent graphical points, "b" is a y-intercept (point where the line hits the y-axis) and "m" is the slope of the line.

Find the intercepts of 7y - 3x = 42. Begin working on getting it into slope intercept form by first adding "3x" to both sides: 7y = 3x + 42. Divide both sides by 7: y = (3x/7) + 6.

Using the rule of the slope intercept form, you should know that the 6 (or "b") is the y-intercept. Show your work anyway and set the x equal to 0 to find the slope intercept: y = (3 * 0/7) + 6 or y = 0 + 6 or y = 6.

Find the x-intercept by setting the y equal to 0, using the original equation for ease of multiplication: 7 * 0 - 3x = 42 or 0 - 3x = 42 or -3x = 42. Divide both sides by "-3" to find the x-intercept: x = -14.

Write down what information you know about the line: y-intercept = 6, x-intercept = -14 and slope is 3/7.

Set up your graph on graph paper so that each line on the x and y axes represents a value of 2, making sure to label the negative axis as well. Draw a dark bubble at point (0, 6), which is the y-intercept and will just be a dot on the "6" line on the y-axis. Draw a dark bubble at point (-14 , 0) which will be -14 on the x-axis.

Find two other points on the line to help draw it by using the slope (3/7). Refer to the definition of a slope being rise over run, or going up followed by going to the right. Begin with the y-intercept point of (0, 6) and count up 3 points and over 7 to find the point (7, 9) and draw a dark bubble there. Do the same for the x-intercept point of (-14, 0) to find the point (-7 , 3), noting that because the number is negative and it is going in a positive direction, it gets "smaller".

Use a ruler to draw the points through each of the lines. Draw an arrow on each end of the line to show that it keeps going beyond what you have graphed.