Answer:
Step-by-step explanation:
The general equation of a line is [tex]y=mx+b[/tex] where m is the slope and b the y intercept.
We have the equation of a line: y=-5x+9. Where [tex]m_1=-5[/tex]
And we have to find [tex]y=m_2x+b_2[/tex]
Two lines are parallel if the slopes are the same, this means [tex]m_1=m_2[/tex]
Then [tex]m_2=-5[/tex]
[tex]y=-5x+b_2[/tex]
We have to find the y intercept. We now that the line passes through (0,8) then we have to replace this point in [tex]y=-5x+b_2[/tex]
[tex]y=-5x+b_2\\8=-5.(0)+b_2\\8=b_2[/tex]
Then the equation of the line that is parallel to y=9-5x and passes through (0, 8) is [tex]y=-5x+8[/tex]
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:
