Question

If y=x-6 where changed to y=x+8 how would the graph of the new function compare with the first one ?

Answer 1

The function
`y=x+8` is the function
`y=x-6` 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)

Explanation:

The equation of the line in slope intercept form is:

`y=mx+b`

Where m is the slope and b is the y-intercept.

The first equation is:

`y=x-6`

The second equation is:

`y=x+8`

The parent function with the form
`y=mx` can be shifted up or shifted down k units.

When
`y=mx+k` the function is shifted k units up.

When
`y=mx-k` the function is shifted k units down.

Then, the function
`y=x+8` is obtained by adding k=14 to the function
`y=x-6`.

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)