Question

Parallel to y=2/3x+4 and goes through (-9,-2)

Answer 1

Hey there :)

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

Since this line is parallel to the line to be found, both have the same slope:
`(2)/(3)`

Coordinates: ( - 9 , - 2 )

y - ( -2 ) =
`(2)/(3)` ( x - ( -9 ) )

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

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


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

Answer 2

Hi there! The answer is y = 2/3x + 4

When the line we are looking for is parallel to y = 2/3x + 4, the slope is the same as in the line mentioned before. Hence, we get the following formula:

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

In this equation, b represents a number. Since the line passes through the point (-9, -2) we can plug in the coordinates into the formula. Then we get the following:

`(2)/(3) * -9 + b = -2`

`-6 + b = -2`

Now we add 6 to both sides of the equation

`b = 4`

We've now found our answer, the formula of the line, which is:
y = 2/3x + 4