Question

(03.03 MC)

The table below represents a linear function f(x) and the equation represents a function g(x):
х f(x)
-1 -5
0 -1
1 3
g(x)
g(x) = 2x - 7

Part A: Write a sentence to compare the slope of the two functions and show the steps you used to determine the slope of f(x) and g(x).
(6 points)
Part B: Which function has a greater y-intercept? Justify your answer. (4 points)
(10 points)

Answer 1

Please check the explanation.

Explanation:

Part a)

Finding the slope of f(x)

Given the table of the function f(x)

x f(x)

-1 -5

0 -1

1 3

Finding the slope using the formula

`\mathrm{Slope}=(y_2-y_1)/(x_2-x_1)`

`\left(x_1,\:y_1\right)=\left(-1,\:-5\right),\:\left(x_2,\:y_2\right)=\left(0,\:-1\right)`

`m=(-1-\left(-5\right))/(0-\left(-1\right))`

`m=4`

Thus, the slope of the function f(x) = 4

Finding the slope of g(x)

We know the slope-intercept form of a linear function is

`y = mx+b`

where m is the slope and b is the y-intercept

Given the function

`g(x) = 2x-7`

comparing with the slope-intercept form

y = mx+b

The slope of the function g(x) = 2

Thus, we conclude that:

• The slope of the function f(x) = 4

• The slope of the function g(x) = 2

Hence, the slope of f(x) is greater.

Part b)

Finding the y-intercept form of f(x)

We know that the y-intercept can be determined by setting x = 0 and determining the corresponding y-value.

From the table,

It is clear at x = 0, y = -1

Hence, the y-intercept of the function f(x) = -1

Finding the y-intercept form of g(x)

Given the function

`g(x) = 2x - 7`

comparing with the slope-intercept form (y = mx+b)

`y = mx+b`

where b is the y-intercept

Hence, the y-intercept of g(x) = b = -7

Thus, we conclude that:

• The y-intercept of the function f(x) = -1

• The y-intercept of the function g(x) = -7

Hence, the y-intercept of f(x) is greater.