Questions: Which of the relationships below represents a function with a greater slope than the function y=1/4 x-3 ?

Transcript text: Which of the relationships below represents a function with a greater slope than the function $y=\frac{1}{4} x-3$ ?

Solution

Step 1: Identify the slope of the given function

The given function is $ y = \frac{1}{2}x - 3 $. The slope of this function is $\frac{1}{2}$.

Step 2: Determine the slopes of the functions in the options

We need to find the slopes of the functions represented by the tables and graphs in options A, B, C, and D.

Option A:

For $ x = 2 $ and $ y = 1 $, and $ x = 4 $ and $ y = -5 $: \[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-5 - 1}{4 - 2} = \frac{-6}{2} = -3 \]

Option B:

For $ x = 6 $ and $ y = 10 $, and $ x = 9 $ and $ y = 16 $: \[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{16 - 10}{9 - 6} = \frac{6}{3} = 2 \]

Option C: