Question

Show all work to write the equations of the lines, representing the following conditions, in the form y = mx + b, where m is the slope and b is the y-intercept:

Part A: Passes through (−2, 2) and parallel to 4x − 3y − 7 = 0 (2 points)

Part B: Passes through (−2, 2) and perpendicular to 4x − 3y − 7 = 0 (2 points)

Answer 1

Part A)
`y=(4)/(3)x+(14)/(3)`

Part B)
`y=-(3)/(4)x+(1)/(2)`

Explanation:

Part A) Passes through (−2, 2) and parallel to 4x − 3y − 7 = 0

we have

`4x-3y-7=0`

Isolate he variable y

`3y=4x-7`

`y=(4)/(3)x-(7)/(3)`

The slope of the given line is

`m=(4)/(3)`

Remember that

If two lines are parallel then their slopes are the same

therefore

The slope of the line parallel to the given line is also

`m=(4)/(3)`

Find the equation of the line in slope intercept form

`y=mx+b`

we have

`m=(4)/(3)`

`point\ (-2,2)`

substitute

`2=(4)/(3)(-2)+b`

solve for b

`b=2+(8)/(3)`

`b=(14)/(3)`

therefore

`y=(4)/(3)x+(14)/(3)`

Part B) Passes through (−2, 2) and perpendicular to 4x − 3y − 7 = 0

we have

`4x-3y-7=0`

Isolate he variable y

`3y=4x-7`

`y=(4)/(3)x-(7)/(3)`

The slope of the given line is

`m=(4)/(3)`

Remember that

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

therefore

The slope of the line perpendicular to the given line is

`m=-(3)/(4)`

Find the equation of the line in slope intercept form

`y=mx+b`

we have

`m=-(3)/(4)`

`point\ (-2,2)`

substitute

`2=-(3)/(4)(-2)+b`

solve for b

`b=2-(3)/(2)`

`b=(1)/(2)`

therefore

`y=-(3)/(4)x+(1)/(2)`