Question

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

Answer 1

- The lines of both functions have the same slope.

- The line of the first function intercepts the y-axis at the point (0,-6) and the line of the new function intercepts the y-axis at the point (0,-8).

- The new graph is the graph of the first function but shifted 2 units down.

Explanation:

The equation of the line in slope-intercept form is:

`y=mx+b`

Where the slope is "m" and the intersection of the line with the y-axis is "b".

Given the function in the form
`y=x-6`, you can identify that:

`m=1\\b=-6`

And from the new function in the form
`y=x-8`, you can identify that:

`m=1\\b=-8`

This means that the lines of both functions have the same slope, but the line of the first function
`y=x-6` intercepts the y-axis at the point (0,-6) and the line of the new function
`y=x-8` intercepts the y-axis at the point (0,-8).

Therefore, the graph of the new function is 2 units below of the function
`y=x-6`, or, in other words, the new graph is the graph of the first function but shifted 2 units down.