Question

Identifying the Slope of a Table or Graph
Which linear functions represent a slope of 4? Check all that apply.
A 2-column table with 4 rows. Column 1 is labeled x with entries 3, 6, 9, 12. Column 2 is labeled y with entries negative 11, 1, 13, 25.
On a coordinate plane, a line goes through points (0, 3) and (5, 4).
A 2-column table with 4 rows. Column 1 is labeled x with entries negative 5, negative 1, 3, 7. Column 2 is labeled y with entries negative 32, 24, 16, 8.
On a coordinate plane, a line goes through points (2, 0) and (3, 4).

Answer 1

The functions with slope 4 are the first table and the line through (2,0) and (3,4).

Work:
- Table 1: Δy = 1 − (−11) = 12 for Δx = 6 − 3 = 3, so slope = 12/3 = 4 (same for each step).
- Line through (0,3) and (5,4): slope = (4−3)/(5−0) = 1/5 (not 4).
- Table 2: y changes are 56, −8, −8 for equal Δx = 4, so it’s not linear (no single slope).
- Line through (2,0) and (3,4): slope = (4−0)/(3−2) = 4.