Answer:
The function [tex]y=x+8[/tex] is the function [tex]y=x-6[/tex] shifted 14 units up.
The graph of the first equation will be a line with slope 1 that intersects the y-axis at point (0,-6)
The graph of the second equation will be a line with slope 1 that intersects the y-axis at point (0,8)
Step-by-step explanation:
The equation of the line in slope intercept form is:
[tex]y=mx+b[/tex]
Where m is the slope and b is the y-intercept.
The first equation is:
[tex]y=x-6[/tex]
The second equation is:
[tex]y=x+8[/tex]
The parent function with the form [tex]y=mx[/tex] can be shifted up or shifted down k units.
When [tex]y=mx+k[/tex] the function is shifted k units up.
When [tex]y=mx-k[/tex] the function is shifted k units down.
Then, the function [tex]y=x+8[/tex] is obtained by adding k=14 to the function [tex]y=x-6[/tex].
Both equation has the same slope, but the y-intercepts are different.
The graph of the first equation will be a line with slope 1 that intersects the y-axis at point (0,-6)
The graph of the second equation will be a line with slope 1 that intersects the y-axis at point (0,8)
