Interpreting Lines:

X and Y Intercepts of a Line

Intercepts are an important part of graphs; they can tell us a lot about our data. For example, y-intercepts often tell us our starting amount. Here are some vocabulary words to help you with this lesson:

X-intercept = where the graph crosses the x-axis, and where y = 0
Y-intercept = where the graph crosses the y-axis, and where x = 0

Video Source (02:48 mins) | Transcript

Practice Problems

Use the following graph to answer questions 1 through 6.

Line A has a negative slope and crosses through the x-axis just to the left of -1 and crosses the y-axis at -4. Line B has a positive slope and goes through the point (0,0). Line C has a negative slope and goes through point (0, 3) and point (1.5, 0). Line D has a positive slope and goes through point (-3, 0) and point (0,1). Line E has a negative slope and goes through point (-5,0) and (0,-2).

What is the y-intercept of line A?
What is the x-intercept of line B?
What is the y-intercept of line B?
What are the x-intercept and y-intercept of line C?
What are the x-intercept and y-intercept of line D?
What are the x-intercept and y-intercept of line E?

Solutions

Y-intercept: \(-4\)
X-intercept: 0
Y-intercept: 0
X-intercept: 1.5
Y-intercept: 3 (Written Solution)

To find the x-intercept, we look for the point where the line crosses the x-axis. The line crosses the x-axis where the x-value is approximately 1.5. The y-value is always 0 for every point on the x-axis so the x-intercept is (1.5, 0).

To find the y-intercept, we look for the point where the line crosses the y-axis. The line crosses the y-axis where the y-value is 3. The x-value is always 0 for every point on the y-axis so the y-intercept is (0, 3).
X-intercept: \(-3\)
Y-intercept: 1 (Written Solution)

To find the x-intercept, we look for the point where the line crosses the x-axis. The line crosses the x-axis where the x-value is approximately \(-3\). The y-value is always 0 for every point on the x-axis so the x-intercept is \(\left ( -3,0 \right )\).

To find the y-intercept, we look for the point where the line crosses the y-axis. The line crosses the y-axis where the y-value is 1. The x-value is always 0 for every point on the y-axis so the y-intercept is (0, 1).
X-intercept: \(-5\)
Y-intercept: \(-2\)