How to Find X-Intercept, Y-Intercept and Intersections
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.
Video Lesson
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Flashcards
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Finding Intercepts from an Equation
- For , setting gives a y-intercept of 200.
- Setting and solving gives the x-intercept of 4.
Intersections of Linear Equations
- An intersection is the point where two lines meet.
- At the intersection, both equations have the same x and y values.
Finding the Intersection Point
- Set the two equations equal to each other to find x.
- Put the value of x back into any equation to find y.
Practice Questions
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In the equation , what is the y-intercept?
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The y-intercept is the constant term in the equation . In this case, the y-intercept is 2, and it is the value of y when .
In the equation , what is the x-intercept?
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The x-intercept is found by setting and solving for x. . Adding to both sides gives . Dividing both sides by 4 gives .
Given the equations and , what is the intersection point?
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To find the intersection, set both equations equal to each other: . Then solve for x: . Now substitute into either equation to find y: . So, the intersection point is (1, 5).
Find the point of intersection of the lines and .
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Set both equations equal to each other: . Then solve for x: . Substitute into either equation to find y: . So, the intersection point is (1, 3).
Find the intersection of the lines and .
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Set both equations equal to each other: . Then solve for x: . Now substitute into either equation to find y: . So, the intersection point is (3, 7).
A car starts with 120 litres of fuel. The car burns 6 litres of fuel every hour. After a few hours, 60 litres of fuel are left. Find out how many hours the car has been driven.
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Form the equation for the remaining fuel: , where is the number of hours. Since 60 litres are left, set and solve for : . Then . So, the car has been driven for 10 hours.
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Interactive Activity
Graph linear equations and find their intersection point
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How to Find X-Intercept, Y-Intercept and Intersections frequently asked questions
The questions students bump into most on this topic
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.
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.
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.
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.
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.