How to Calculate Intersecting
Calculating the intersection point for two lines, also called linear functions, is a simple mathematical process that is taught in high school or earlier algebra. The intersection point is the point where the two lines cross each other. At this point the x and y coordinates will be identical for both lines. Coordinates are displayed as (x, y), and each point on the graph of a line has a different set of coordinates. How to calculate the intersection point will be explained through calculating the intersection coordinates of a sample problem.
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Instructions
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1
Find the equations for the two lines that intersect. The equation will be in the slope-intercept format of y = mx+ b, where m equals the slope and b equals the y-intercept.
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2
Set the two equations equal to each other. For example, if your equations are y = 2x + 3 and y = 4x + 6, once you set them equal to each other it will look like 2x + 3 = 4x + 6.
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3
Solve for the x variable by isolating the x variable on one side of the equation. For the equation listed in Step 2, solving for the x variable requires the following steps:
2x + 3 = 4x + 6
2x = 4x + 6 - 3 (subtract 3 from both sides)
2x - 4x = 6 - 3 (subtract the x variable from both sides)
-2x = 3
x = 3/-2 (get x by itself by dividing both sides by -2)
x = -3/2 or -1.5 -
4
Plug the x value back into the original equations to solve for y. The coordinates will be the same for both equations, but perform the calculations on both equations to check your work and make sure the y value is the same.
y = 2(-1.5) + 3 and y = 4(-1.5) + 6
y = -3 + 3 and y = -6 +6
y = 0 and y = 0
The y values for both equations equal 0. You have checked your work and made sure the answer is correct. -
5
Take the answers from steps 3 and 4 to get your intersection point. The x value at the intersection point is -1.5 and the y value at the intersection point is 0. The intersection coordinates are (-1.5,0).
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