Question

Which function has the greatest rate of change?

A.
6x – 3y = 12

B.
y = 5x + 4

C.
x y
1 2
3 8
5 14

okay so i know how to find slope intercept form, and how to know if its negative or positive rate of change, but im not sure how i know which has the greatest?

Answer 1

solve A for "y"
B is already solved for "y"

so.. what do you get for A?

Answer 2

hmm I think by "greatest", they mean the "steepest", regardless of sign

Answer 3

i was thinking maybe they ment the biggest slope?

Answer 4

could be, is rather ambiguous, but slope wise, I'd think they mean the steepest, since a negative slope is as vald and legitiimate as a positive slope

Answer 5

as far as getting the slope for C, well, use the rise/run to get it
say

C.
x y
1 2
3 8 <--- using this point
5 14 <--- and this point

then you get the slope by \(\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
&({\color{red}{ 3}}\quad ,&{\color{blue}{ 8}})\quad
% (c,d)
&({\color{red}{ 5}}\quad ,&{\color{blue}{ 14}})
\end{array}
\\\quad \\
% slope = m
slope = {\color{green}{ m}}= \cfrac{rise}{run} \implies
\cfrac{{\color{blue}{ y_2}}-{\color{blue}{ y_1}}}{{\color{red}{ x_2}}-{\color{red}{ x_1}}}\)

Answer 6

Well so far with what I've done A has been crossed out cause it's a wrong answer

Answer 7

there cant be a wrong answer just which one has the greatest rate of change

Answer 8

-6/-2 turns into -3/-1

so -3 for the slope on C? or since there both negatives its positive?