Question

PLEASE HELP WITH #11! (Please explain as well? Even a brief explanation is fine.) THANK YOUU.

Answer 1

10) f(x) = mx + b is a linear equation passing by the point b (on y-axis)

In the example f(x) = 4x means that b=0 & hence it passes by the origin, It is always increasing since its coefficient (or the slope) is positive & equal 4.

So the answer is F

11) the highest the coefficient (or slope) the greater is the rate of change , so it is answer I with m=4 (which is greater than (-1/2)

Answer 2

The functions given are of the form y=mx+b where m is the slope, which is the rate of change.

I dy/dx=4 you can tell by the slope that the rate of change is 4

II dy/dx=1/2 for the same reason as above

III for this one you need to calculate slope or m

m=(y2-y1)/(x2-x1)

from a few points (12-6)/(2-1)=(18-12)/(3-2)=m=6

So function III has the greatest rate of change.