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 = 0.5x - 7 and y = -4x + 20 intersect. The first step is to set the equations equal to each other and solve for x
0.5x - 7 = -4x + 20
4.5x = 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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