Question

Let line L be given by the equation Ax + By = C.

A. Write the equation, in slope intercept form, of the line passing through the point (2, 7) and parallel to line L.

B. Write the equation, in slope intercept form, of the line passing through the point (2, 7) and perpendicular to line L.

Answer 1

Part A)
`y=-(A)/(B)x+(7B+2A)/(B)`

Part B)
`y=(B)/(A)x+(7A-2B)/(A)`

Explanation:

we have the equation of the line L in standard form

`Ax+By=C`

isolate the variable y

`By=-Ax+C`

`y=-(A/B)x+C/B`

The slope of the line L is equal to

`m=-A/B`

Part A) Write the equation, in slope intercept form, of the line passing through the point (2, 7) and parallel to line L

Remember that

If two line are parallel, then their slopes are equal

The equation of the line in slope intercept form is equal to

`y=mx+b`

we have

`m=-A/B`

`point (2,7)`

substitute the values and solve for b

`7=(-A/B)(2)+b`

`b=7+2A/B=(7B+2A)/B`

The equation of the line is

`y=-(A)/(B)x+(7B+2A)/(B)`

Part B) Write the equation, in slope intercept form, of the line passing through the point (2, 7) and perpendicular to line L

Remember that

If two line are perpendicular, then the product of their slopes is equal to -1

`m1*m2=-1`

The equation of the line in slope intercept form is equal to

`y=mx+b`

we have

`m1=-A/B`

Find the value of m2

`(-A/B)*m2=-1`

`m2=B/A`

`point (2,7)`

substitute the values and solve for b

`7=(B/A)(2)+b`

`b=7-2B/A=(7A-2B)/A`

The equation of the line is

`y=(B)/(A)x+(7A-2B)/(A)`