Question

Below are two different functions, f(x) and g(x). What can be determined about their slopes?

f(x) George reads 200 pages in 40 minutes.
x g(x)
4 -8
4 10
4 28
(1 point)
The function f(x) has a larger slope.
The relationship between slopes cannot be determined.
They both have the same slope.
0
The function g(x) has a larger slope.

Answer 1

The relationship between slopes cannot be determined ⇒ (B)

Explanation:

Let us revise some important fact about the slope of a line

The slope of a line is the ratio between the vertical change and the horizontal change (Δy/Δx)

• The slope is positive if the vertical and horizontal changes are increasing together or decreasing together
• The slope is negative if the vertical and horizontal changes are opposite (if one increases the other decreases)
• The slope is zero if the vertical change is zero (represented by a horizontal line)
• The slope is undefined if the horizontal change is zero (represented by a vertical line)

Let us solve the question

∵ George can reed 200 pages in 40 minutes

∴ The slope of f(x) represents the rate of reading of George

∴ The slope of f(x) = 200/40 = 5 pages per minutes

∵ The given table represents g(x)

∴ Points (4, -8), (4, 10), and (4, 28) belong to g(x)

∵ All the points have the same x-coordinates

→ That means the change in x = 0 (horizontal change)

∴ g(x) represented by a vertical line

∴ g(x) has no slope

→ That means we can not compare between the slopes

of f(x) and g(x)

∴ The relationship between slopes cannot be determined