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Aleonysh [2.5K]
1 year ago
8

What is the slope of a line that is perpendicular to the line whose equation is ax by=c?

Mathematics
1 answer:
fiasKO [112]1 year ago
6 0

Answer:

b/a

Step-by-step explanation:

Perpendicular lines have slopes that are opposite sign and reciprocals (flipped over).

In the equation

ax + by = c,

the slope of the line is

-a/b

If you haven't memorized this pattern yet, you can calculate it by solving ax+by=c for y.

by = -ax +c

y = -a/b x + c/b

The slope is -a/b

So a perpendicular line would be opposite sign and flipped, b/a

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The basic structure of a linear function is y=mx+b (or +c, depending on your schools curriculum)

We need to find the slope (m), and the y-intercept (b/c)

To find the slope you can pick two random points, say (2,2) and (0,1)

The formula for the slope is this: m= y1-y2 / x1-x2

So if we substitute the points in, we get 2-1 / 2-0 = 1/2

Knowing the slope, it can be substituted into to the equation: y=1/2x + b

Then, if you notice the second point- (0,1), it’s the y-intercept. The y coordinate there is 1.

To check if this is correct, a random coordinate set can be picked and substituted in to find b.

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