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Consider the line . 7x-8y=-1Find the equation of the line that is parallel to this line and passes through the point . (-3,-6)Find the equation of the line that is perpendicular to this line and passes through the point . (-3.-6)

Consider The Line 7x8y1Find The Equation Of The Line That Is Parallel To This Line And Passes Through The Point 36Find The Equation Of The Line That Is Perpendi class=

Sagot :

we have the line

7x-8y=-1

Find out the slope of the given line

isolate the variable y

8y=7x+1

y=(7/8)x+1/8

the slope is m=7/8

Part a

Find the equation of the line that is parallel to this line and passes through the point . (-3,-6)

Remember that

If two lines are parallel, then their slopes are equal

so

The slope of the parallel line is m=7/8 too

Find out the equation of the line in slope-intercept form

y=mx+b

we have

m=7/8

point (-3,-6)

substitute and solve for b

-6=(7/8)(-3)+b

b=-6+(21/8)

b=-27/8

therefore

The equation is

y=(7/8)x-27/8

Part b

Find the equation of the line that is perpendicular to this line and passes through the point . (-3.-6)

Remember that

If two lines are perpendicular, then their slopes are negative reciprocal

so

The slope of the perpendicular line is m=-8/7

Find out the equation of the line in slope-intercept form

y=mx+b

we have

m=-8/7

point (-3,-6)

substitute and solve for b

-6=-(8/7)(-3)+b

b=-6-(24/7)

b=-66/7

therefore

the equation is

y=-(8/7)x-66/7

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