How to Find & Graph Intercepts


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.

Things You'll Need

  • Graph paper
  • Ruler
  • 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.

Tips & Warnings

  • Negative numbers on the x-axis are found to the left hand side of the origin, where the axises connect. Negative numbers on the y-axis are found directly below the origin.


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