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Sedbober [7]
2 years ago
10

Two perpendicular lines have opposite y-intercepts. The equation of one of these lines is y = mx + b. Express the x-coordinate o

f the intersection point of the lines in terms of m and b.
Mathematics
1 answer:
Fofino [41]2 years ago
6 0

Answer:

x = -2bm/(m²+1)

Step-by-step explanation:

One line has equation

... y = mx + b

The slope of the perpendicular line is the negative reciprocal of the slope of the original line. The perpendicular line with the opposite y-intercept has equation

... y = (-1/m)x - b

The point of intersection is where the x- and y-values are equal, so ...

... mx + b = (-1/m)x - b

... (m +1/m)x = -2b . . . . . . . add 1/m - b to both sides

... (m²+1)x = -2bm . . . . . . . multiply by m

... x = -2bm/(m²+1) . . . . . . divide by the coefficient of x

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