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

Answer:

-  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.

Step-by-step 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.