Question

The table below represents a linear function f(x) and the equation represents a function g(x):

x f(x)
−1 −3
0 0
1 3
g(x)

g(x) = 7x + 2


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)

Answer 1

A: Looking at the last two rows of the table of f(x), the slope is simply (3-0)/(1-0) = 3, while the slope of g(x) is the coefficient of the variable x, which is 7.

B. y-int is the y value when x = 0. f(x) has a y-int of 0, which g(x) is 2. The latter has a greater y-int.

Answer 2

Part A: The slope of g(x) is greater than the slope of f(x).

Part B: Function g(x) has greater y-intercept.

Explanation:

The function f(x) passes through the points (-1,-3), (0,0) and (1,3). It means the y-intercept of the function is 0.

If a line passes through two points, then the slope of the function is

`m=(y_2-y_1)/(x_2-x_1)`

Let as consider any two points of the function, (-1,-3) and (0,0).

`m=(0+3)/(0+1)=3`

The point slope form of a linear function is

`m=mx+b` .... (1)

Where, m is slope and b is y-intercept.

The slope of f(x) is 3 and y-intercept is 0, therefore the function f(x) is

`f(x)=3x`

The given function is

`g(x)=7x+2` .... (2)

From (1) and (2), we get

`m=7,b=2`

The slope of g(x) is 3 and y-intercept is 2.

Part A: Since the slope of f(x) is 3 and the slope of g(x) is 7, therefore the slope of g(x) is greater than the slope of f(x).

Part B: Since the y-intercept of f(x) is 0 and y-intercept of g(x) is 2, therefore the function g(x) has greater y-intercept.