322,127 views
36 votes
36 votes
8A. A line goes through the point (-7. 1) and is parallel to -3y+7x12. Find an equation in pointslope form and find the equation in slope intercept form. Be sure to show your work.B. A line goes through the point (3, 4) and is perpendicular to 5x9y 1. Find an equation inpoint slope form and find the equation in slope intercept form. Be sure to show your work

User Kiku
by
2.8k points

1 Answer

11 votes
11 votes

A line goes through point (-7,1) and is parallel to -3y+7x=12. Find a equation in point slope form and find equation in slope intercept form. Show your work

step 1

Find the slope of the given line

-3y+7x=12

isolate the variable y

3y=7x-12

y=(7/3)x-4

slope is m=7/3

step 2

Remember that

If two lines are parallell , then their slopes are equal

so

the slope of the parallel line is m=7/3

Find the equation in point slope form

y-y1=m(x-x1)

we have

m=7/3

point (-7,1)

substitute

y-1=(7/3)(x+7) -------> equation in point slope form

step 3

Find the equation in slope intercept form

y=mx+b

we have

m=7/3

point (-7,1)

substitute

1=(7/3)(-7)+b

1=-49/3+b

b=52/3

therefore

y=(7/3)x+52/3 ------> equation in slope intercept form

Problem N 2

A line goes through the point (3,-4) and is perpendicular to 5x+9y=1. Find an equation in point slope form and find equation in slope intercept form

step 1

Find the slope of the given line

5x+9y=1

9y=-5x+1

y=-(5/9)x+1/9

slope is m=-5/9

step 2

slope of the parallel line is m=-5/9

equation in point slope form is

y+4=-(5/9)(x-3)

step 3

equation in slope intercept form is

y=mx+b

m=-5/9

point (3.-4)

-4=-(5/9)(3)+b

-4=-(5/3)+b

b=-4+5/3

b=-7/3

therefore

y=-(5/9)x-7/3

User Jake
by
2.5k points