Mathematics: Consider the line y = -8x+ find the equation of the line that is perpendicular to this line and passes through the point (-4, 4). find the equation of the line that is parallel to this line and passes through the point (-4, 4). equation of perpendicular line: equation of parallel line:

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Consider the line y = -8x+ find the equation of the

Ответ:

e03per503

12.01.2022

Mathematics

Part 1) The equation of the perpendicular line is $y=\frac{1}{8}x+\frac{9}{2}$

Part 2) The equation of the parallel line is y=-8x-28

Step-by-step explanation:

Part 1) Find the equation of the line that is perpendicular to the given line and passes through the point (-4, 4)

The slope of the given line is m=-8

Remember that

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of the slopes is equal to -1)

The slope of the line perpendicular to the given line is

$m=\frac{1}{8}$

Find the equation of the perpendicular line in point slope form

y-y1=m(x-x1)

we have

$m=\frac{1}{8}$

$point\ (-4,4)$

substitute

$y-4=\frac{1}{8}(x+4)$

Convert to slope intercept form

y=mx+b

isolate the variable y

apply distributive property right side

$y-4=\frac{1}{8}x+\frac{1}{2}$

$y=\frac{1}{8}x+\frac{1}{2}+4$

$y=\frac{1}{8}x+\frac{9}{2}$

Part 2) Find the equation of the line that is parallel to the given line and passes through the point (-4, 4)

The slope of the given line is m=-8

Remember that

If two lines are parallel, then their slopes are the same

The slope of the line parallel to the given line is

m=-8

Find the equation of the parallel line in point slope form

y-y1=m(x-x1)

we have

m=-8

$point\ (-4,4)$

substitute

y-4=-8(x+4)

Convert to slope intercept form

y=mx+b

isolate the variable y

apply distributive property right side

y-4=-8x-32

y=-8x-32+4

y=-8x-28

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Consider the line y = -8x+
find the equation of the line that is perpendicular to this line and passes through the point (-4, 4).
find the equation of the line that is parallel to this line and passes through the point (-4, 4).
equation of perpendicular line:
equation of parallel line:

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