# How to Calculate the Intersection of Two Lines

Equations in the form *y = mx + b* represent lines in the *xy*-plane. The value of *m* is the slope of the line, i.e., the rise over the run. The value of *b* is the *y*-intercept, that is, the point where the line crosses the *y*-axis. If two lines have distinct slopes, then they will have a unique intersection point.

To find the intersection point of two lines, you must solve a system of two equations. For example, suppose you want to determine where the lines *y* = 0.5*x* - 7 and *y* = -4*x* + 20 intersect. The first step is to set the equations equal to each other and solve for *x*

0.5*x* - 7 = -4*x* + 20

4.5*x* = 27

*x* = 27/4.5 = 6

So the *x*-coordinate of the intersection point is 6. To find the *y*-coordinate, plug 6 into one of the original equations.

*y* = 0.5(6) - 7

*y* = 3 - 7

*y* = -4.

So the intersection point is (6, -4).

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