Definition: The y-intercept is the point where a graph crosses the y-axis, where x equals zero, and in y = mx + b it is the value b.
What is the y-intercept?
It is the place a line meets the vertical axis. At that point, x = 0, so the point looks like (0, b).
How do you find it?
From an equation, substitute x = 0. For y = 4x – 9, the y-intercept is -9, at the point (0, -9). From a graph, read where it crosses the vertical axis. From a table, look at the row where x is 0.
What does it mean in context?
It is the starting value. A gym charges a 25 dollar sign-up fee plus 12 dollars a month. Cost = 12m + 25, and the y-intercept 25 is the cost at zero months.
How is it related to proportional lines?
A proportional line has y-intercept 0, because it passes through the origin.
How do you use it with a point?
If a line has slope 3 and passes through (2, 11), then 11 = 3(2) + b gives b = 5.
What is a common mistake?
Reading the y-intercept as the x-value. The y-intercept is the output, y, at x = 0. The point where the line crosses the x-axis is a different thing, the x-intercept.
Where to learn it
- Solving Multi-Step Linear Equations – lesson
- Modeling Real Situations With Linear Functions – lesson