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45 votes
Find an equation of the line that satisfies the given conditions.

Through (-1, -6); perpendicular to the line passing through (2, 6) and (6, 4)

User Chirag Dasani
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2.6k points

2 Answers

6 votes
6 votes

Answer:

Slope would be 5 and y-intercept would be 2

Explanation:

I just solved it in my head

User Joe Majewski
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2.5k points
13 votes
13 votes

Answer:

y = 2x-4

Explanation:

This has already been answered correctly by aechristman27, but I'll add some of the details.

The equation of a line perpendicular to a reference equation has a slope that is the negative inverse of the referenced line's slope.

Reference line:

We are only given two points on the reference line. We need the slope of this line, which we can find from the two given points.

The slope is the Rise/Run (The change in y for a change in x)

Use the two points:

(2,6) and (6,4)

Rise = (4-6) = -2

Run = (6-2 = 4

Slope = Rise/Run = -2/4 or -(1/2)

The new slope is the negative inverse of -(1/2), which makes the new slope 2.

The new line is then y = 2x + b.

To find b, we can use the one given point on this line: (-1,-6). Enter that point ion the equation and solve for b:

y = 2x + b

-6 = 2(-1) + b for (-1,-6)

-6 = -2 + b

b = -4

The equation is y = 2x-4

See the attached graph.

Find an equation of the line that satisfies the given conditions. Through (-1, -6); perpendicular-example-1
User Johnny Graettinger
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3.3k points