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Determine the equation of the line that passes through the point15and is perpendicular to the line y = -4x + 2.4(5,-5)Enter your answer in slope-intercept form.

Determine the equation of the line that passes through the point15and is perpendicular-example-1
User Vishnu Vinod
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1 Answer

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26 votes

The equation of a line in the slope intercept form is expressed as

y = mx + c

where

m represents slope

c represents y intercept

From the information given,

The equation of the line to be determined is perpencicular to the line

y = -4x + 2

By comparing this equation with the slope intercept equation,

slope = - 4

If two lines are perpendicular, it means that the slope of one line is the negative reciprocal of the slope of the other line. The negative reciprocal of - 4 is 1/4. Thus, the slope of the line passing through (5, - 15/4) is 1/4. We would find the y intercept, c of this line by substituting m = 1/4, x = 5 and y = - 15/4 into the slope intercept equation. We have

- 15/4 = 1/4 * 5 + c

- 15/4 = 5/4 + c

c = - 15/4 - 5/4 = (- 15 - 5)/4 = - 20/4

c = - 5

By substituting m = 1/4 and c = - 5 into the slope intercept equation, the equation of the line that passes through (5, - 15/4) and is perpendicular to the line, y = - 4x + 2 is

y = x/4 - 5

User Aredzko
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