Question

Both functions are linear
Function A: y = x +5
Function B: Has a y-intercept of (0, 3)
Which one is greater

Answer 1

You cannot tell from the information given — the slope of function B is not specified. Let B be y = m x + 3. Compare:

x + 5 > m x + 3 ⇔ (1 − m)x > −2.

- If m = 1 (so B is y = x + 3), then x + 5 > x + 3 for all x, so A is always greater (by 2).
- If m < 1, then 1 − m > 0 and A > B for x > −2/(1 − m).
- If m > 1, then 1 − m < 0 and A > B for x < 2/(m − 1).

The two graphs meet at x = −2/(1 − m). Give the slope of B (m) and I can tell you which function is greater for which x.