Question

Comparing Linear Functions Written in Different Ways
A 2-column table with 4 rows. Column 1 is labeled x with entries 5, 3, negative 1, negative 2. Column 2 is labeled y with entries 6, 2, negative 6, negative 8. On a coordinate plane, a line goes through points (negative 2, 4) and (0, negative 4).

Linear functions are expressed by data in a table and by a graph. Select all that apply.
The slope is the same for both functions.
The function expressed in the graph has a steeper slope than the function in the table.
The y-intercept is the same for both functions.
The table and the graph express an equivalent function.

Answer 1

Correct choices:
- The function expressed in the graph has a steeper slope than the function in the table.
- The y-intercept is the same for both functions.

Reasoning:
- From the table the points give slope = (2−6)/(3−5)=2, so the table function is y = 2x − 4.
- From the graph the line through (−2,4) and (0,−4) has slope = (−4−4)/(0−(−2)) = −8/2 = −4 and y-intercept −4, so y = −4x − 4.
- Both have y-intercept −4, but slopes 2 and −4 differ; |−4|>2 so the graphed line is steeper.