Question

Comparing the Steepness of the Slope of Linear Functions
Which linear function has the steepest slope?
On a coordinate plane, a line goes through points (0, 3) and (4, 2).
y = negative 0.1 x minus 5
A 2-column table with 5 rows. Column 1 is labeled x with entries negative 4, negative 2, 0, 2, 4. Column 2 is labeled y with entries 0, 0.5, 1.0, 1.5, 2.0.
A 2-column table with 5 rows. Column 1 is labeled x with entries negative 6, negative 2, 1, 7, 9. Column 2 is labeled y with entries 6.6, 4.2, 2.4, negative 1.2, negative 2.4.

Answer 1

Find each slope (steepness = |slope|) and compare:

- Line through (0,3) and (4,2): m = (2−3)/(4−0) = −1/4 = −0.25 (|m| = 0.25).
- y = −0.1x − 5: m = −0.1 (|m| = 0.1).
- Table 1 (x: −4,−2,0,2,4; y: 0,0.5,1.0,1.5,2.0): slope = 0.5/2 = 0.25 (|m| = 0.25).
- Table 2 (x: −6,−2,1,7,9; y: 6.6,4.2,2.4,−1.2,−2.4): slope = (4.2−6.6)/(−2−(−6)) = −2.4/4 = −0.6 (|m| = 0.6).

The steepest slope is from the last table (slope = −0.6).