x-intercept and y-intercept of a line
The x-intercept and y-intercept of a line are the points where a line crosses the coordinate axes. From OpenStax Elementary Algebra 2E, Chapter 4, the x-intercept is the point (a, 0) where the line crosses the x-axis, found by setting y=0. The y-intercept is the point (0, b) where the line crosses the y-axis, found by setting x=0. For example, a line with x-intercept (9,0) crosses the x-axis at x=9, and a line with y-intercept (0,-5) crosses the y-axis at y=-5. These two key points are essential for graphing lines and interpreting linear equations in algebra.
Key Concepts
Property The $x$ intercept is the point $(a, 0)$ where the line crosses the $x$ axis.
The $y$ intercept is the point $(0, b)$ where the line crosses the $y$ axis.
The $x$ intercept occurs when $y$ is zero.
Common Questions
What is the x-intercept of a line?
The x-intercept is the point (a, 0) where the line crosses the x-axis. It always has a y-coordinate of zero.
How do you find the y-intercept from an equation?
Set x=0 in the equation and solve for y. The result gives the point (0, b), which is the y-intercept.
What is the y-coordinate of any x-intercept?
The y-coordinate of every x-intercept is always 0, because the x-axis is defined as y=0.
How do you find the x-intercept of a linear equation?
Substitute y=0 into the equation and solve for x. The answer gives the point (a, 0) where the line meets the x-axis.
If a line has x-intercept (2,0) and y-intercept (0,10), what does that mean?
The line crosses the x-axis at x=2 and the y-axis at y=10. You can use these two points to graph the line.