How to Find X-Intercept, Y-Intercept and Intersections

Q: How do you find the y-intercept?

Set x to 0 in the equation, then read off the value of y. For Amy's journey y = 200 - 50x, putting x = 0 gives y = 200. So the y-intercept is 200. On a graph, this is where the line crosses the y-axis.

Q: How do you find the x-intercept?

Set y to 0 and solve the equation for x. For Amy's journey, 0 = 200 - 50x rearranges to 50x = 200, so x = 4. The x-intercept is 4, the point where the line crosses the x-axis, when no distance remains.

Q: What does the y-intercept represent?

The y-intercept represents the starting value before anything changes. In Amy's journey, a y-intercept of 200 confirms her original distance is 200 miles. That is how far she still has to travel when x = 0, before she has driven at all.

Q: Can you find the point of intersection without a graph?

Yes. Set the two equations equal to each other and solve for x. Then substitute that x value into either equation to find y. For Amy and Bobby, this gives (2.5, 75), the same answer the graph shows, without drawing one.

Q: Which equation should you substitute into to find y?

You can substitute the x value into either equation, because both lines meet at the same point. Choose the equation with the smaller numbers to keep the arithmetic simple. For Amy and Bobby, Bobby's equation y = 150 - 30x is easier. It gives y = 75 when x = 2.5.

Key concept

The x-intercept is found by setting y = 0, and the y-intercept by setting x = 0. For y = 200 − 50x, this gives an x-intercept of 4 and a y-intercept of 200. Two lines intersect where they share the same x and y values.

How to Find X-Intercept, Y-Intercept and Intersections - introduction visual

Video Lesson

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$How to Find X-Intercept, Y-Intercept and Intersections poster$

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Flashcards

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Diagram explaining the x- and y-intercepts of linear equations using the equation y = 200 - 50x, illustrating where the line crosses the axes.

Intersection of two linear equations, y = 200 - 50x and y = 150 - 30x, at point (2.5, 75) with x-axis as hours drove and y-axis as remaining distance.

Steps to find the intersection of two linear equations by setting equations equal and solving for x and y, with equations and example values.

Finding Intercepts from an Equation

For $y = 200 - 50 x$ , setting $x = 0$ gives a y-intercept of 200.
Setting $y = 0$ and solving $0 = 200 - 50 x$ gives the x-intercept of 4.

Practice Questions

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Q1Easy

In the equation $y = 3 x + 2$ , what is the y-intercept?

Choose your answer to continue

Interactive Activity

Graph linear equations and find their intersection point

Enter Equations

Line 1

y =x +

Line 2

y =x +

Finding Intersection

Set equations equal:

x + 1 = -x + 5

Solve for x:

2x = 4x = 2

Substitute x to find y:

y = 3

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Students Also Ask

The questions students bump into most on this topic

How do you find the y-intercept?

Set x to 0 in the equation, then read off the value of y. For Amy's journey y = 200 - 50x, putting x = 0 gives y = 200. So the y-intercept is 200. On a graph, this is where the line crosses the y-axis.

How do you find the x-intercept?

Set y to 0 and solve the equation for x. For Amy's journey, 0 = 200 - 50x rearranges to 50x = 200, so x = 4. The x-intercept is 4, the point where the line crosses the x-axis, when no distance remains.

What does the y-intercept represent?

The y-intercept represents the starting value before anything changes. In Amy's journey, a y-intercept of 200 confirms her original distance is 200 miles. That is how far she still has to travel when x = 0, before she has driven at all.

Can you find the point of intersection without a graph?

Yes. Set the two equations equal to each other and solve for x. Then substitute that x value into either equation to find y. For Amy and Bobby, this gives (2.5, 75), the same answer the graph shows, without drawing one.

Which equation should you substitute into to find y?

You can substitute the x value into either equation, because both lines meet at the same point. Choose the equation with the smaller numbers to keep the arithmetic simple. For Amy and Bobby, Bobby's equation y = 150 - 30x is easier. It gives y = 75 when x = 2.5.

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