Question

If y = 2x + 7 were changed to y = 12x + 7, how would the graph of the new function compare with the original?

Answer 1

The correct answer is:

C) It would be steeper.

Explanation:

These equations are in slope-intercept form.  

Slope-intercept form is y=mx+b, where m is the slope and b is the y-intercept.

The change from y=2x+7 to y=12x+7 is that 2 is changed to 12.  Both 2 and 12 are in the place of m, meaning they are the slope.

This means the y-intercept stays the same; they start in the same position.

The slope, or rate of change, changes from 2 to 12.  Since both are positive, the line will continue to point up (increase).  However, an increase in slope means the line will increase more quickly, which results in a steeper line.

Answer 2

The x value governs the steepness of the line, so 12x is steeper than 2x

So the answer is C