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

-  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:

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

Given the function in the form , you can identify that:

And from the new function in the form  , you can identify that:

This means that the lines of both functions have the same slope, but 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).

Therefore, the graph of the new function is 2 units below of the function , or, in other words, the new graph is the graph of the first function but shifted 2 units down.

(x+3)(x+7)

step-by-step explanation:

b

step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, 4) and (x₂, y₂ ) = (3, - 5) ← 2 points on the line

m = = = - 3

with m = - 3 and (a, b) = (3, - 5), then

y - (- 5) = - 3(x - 3), that is

y + 5 = - 3(x - 3) → b