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

Answer:

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)

Step-by-step 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)