If y= 12x + 7 were changed to y = 12x + 2, how would the graph of the new function compare with the original?
A. It would be less steep.
B. It would be steeper.
C. It would be shifted down.
D. It would be shifted up.

C. It would be shifted down.

General Formulas and Concepts:

Algebra I

Reading a Cartesian Plane

Functions

Graphing

Coordinates (x, y)

The y-intercept is the y value when x = 0. Another way to reword that is when the graph crosses the y-axis.

Slope-Intercept Form: y = mx + b

Step-by-step explanation:

Step 1: Define

[Original Function] y = 12x + 7

[Transformed Function] y = 12x + 2

Step 2: Identify

Compare functions to general form.

[Original Function] Slope m = 12, y-intercept b = 7

[Transformed Function] Slope m = 12, y-intercept b = 2

Step 3: Compare

We see that they both have the same slope m of 12, so A and B can be eliminated as the slopes don't change and therefore would not be steeper or less steep.

Now comparing the y-intercept b's, we see that the original function has a bigger b than the transformed function. This tells us that the original function will start higher than the transformed function.

We can also graph both equations and see what happens to the original equation.

∴ the answer would be C. It would be shifted down.

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