Question

Please help, I don't really understand.

Answer 1

y =
`(2)/(3)` x +
`(26)/(3)`

y =
`(-3)/(2)` x

Explanation:

y =
`(-3)/(2)` x - 6

The slope of this line is -3/2

A perpendicular slope is the opposite reciprocal. That means you flip it upside down and take the opposite sign. Since this slope is negative, the perpendicular slope will be positive. If I turn this fraction upside down it will be 2/3, so the perpendicular slope is 2/3.

For the equation of the line we need the slope (m) and the y intercept. To find that we will use the point that goes through this line.

m = (2/3)

x = -4 from the point given (-4, 6)

y = 6 from the point given (-4,6)

y = mx + b

6 =
`(2)/(3)`
`((-4)/(1))` + b

6 =
`(-8)/(3)` + b Add
`(8)/(3)` to both sides

`(6)/(1)` +
`(8)/(3)` = b

`(18)/(3)` +
`(8)/(3)` = b

`(26)/(3)`

y =
`(2)/(3)` x +
`(26)/(3)`

Parallel lines have the same slope.

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

x = -4 from the point (-4,6)

y = 6 from the point (-4,6)

y = mx + b

6 =
`(-3)/(2)`
`((-4)/(1))` + b

6 = 6 + b Subtract 6 from both sides

0 = b

y =
`(-3)/(2)` x