Question

What is an equation of the line that is parallel to y = 3x - 8 and passes

through the point (4,-5)?

Answer 1

y = 3 x + 11

Explanation:

Parallel lines have the same slopes.

The slope of the new line will have the same slope as the given line:

y = 3 x − 4

⇒ m = 3

One point on the line is given,

( − 2 5 ) .

This is ( x 1 y 1 )

The formula for slope is

m = ( change in y values/ change in x-values ) = y 2 − y 1/ x 2 − x 1

If you have the slope and one point , substitute them into a formula which is based on the formula for slope given above.

y − y 1 = m ( x − x 1 )

y − 5 = 3 ( x − ( − 2 ) )

y − 5 = 3 ( x + 2 )

Simplify to get the required equation of the line.

y = 3 x + 6 + 5

y = 3 x + 11

Explanation:

Answer 2

`y=3x-17`

Explanation:

Parallel equations always share a slope.

So since we know the slope and a point the equation needs to pass through we can plug in the values and replace -8 with
`b`

`-5=3(4)+b`

simplify both sides

`-5=12+b`

isolate the variable

`-17=b`

plug
`b` back into the equation and you get

`y=3x-17`