Question

he table and graph describe two linear functions.



Function 1



x y
−
2
8
−
1
5
0
2
1
−
1
2
−
4


image.png






Which of the following statements is true?


Function 1 has a greater slope and a greater y-intercept than Function 2.


Function 1 has a greater slope but a lesser y-intercept than Function 2.


Function 2 has a greater slope and a greater y-intercept than Function 1.


Function 2 has a greater slope but a lesser y-intercept than Function 1.

Answer 1

I can’t see the graph you referenced. From the table, Function 1 has slope m1 = (5−8)/(−1−(−2)) = −3 (every time x increases by 1, y decreases by 3) and y‑intercept b1 = 2.

To pick the correct statement you need the slope m2 and y‑intercept b2 of Function 2 (read two clear grid points on the line to compute slope = (rise)/(run), and read y at x=0 for the intercept). Once you have m2 and b2 compare:

- If m1 > m2 then Function 1 has the greater slope; if m1 < m2 then Function 2 does.
- If b1 > b2 then Function 1 has the greater y‑intercept; if b1 < b2 then Function 2 does.

If you upload the graph or tell me two points on Function 2 (or its y-value at x=0), I’ll compute m2 and b2 and tell you which choice is correct.