Question

What is an equation of the line that is parallel to y=9-5x and passes through (0, 8)?

Answer 1

The slope of the given line is the x-coefficient, -5. Then, in point-slope form an equation for the line you want is
y - 8 = -5(x - 0)

This simplifies to
y = 8 -5x

Answer 2

Explanation:

The general equation of a line is
`y=mx+b` where m is the slope and b the y intercept.

We have the equation of a line: y=-5x+9. Where
`m_1=-5`

And we have to find
`y=m_2x+b_2`

Two lines are parallel if the slopes are the same, this means
`m_1=m_2`

Then
`m_2=-5`

`y=-5x+b_2`

We have to find the y intercept. We now that the line passes through (0,8) then we have to replace this point in
`y=-5x+b_2`

`y=-5x+b_2\\8=-5.(0)+b_2\\8=b_2`

Then the equation of the line that is parallel to y=9-5x and passes through (0, 8) is
`y=-5x+8`

In the graph of the lines where y=-5x+9 is pink and y=-5x+8 is green, you can see that they are parallels: