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

Answer:

Please check the explanation.

Step-by-step 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

$\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}$

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

$m=\frac{-1-\left(-5\right)}{0-\left(-1\right)}$

$m=4$

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.