Question

Someone please take your time to help me, I very much appreciate it.

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


x f(x)
−1 −7
0 −1
1 5
g(x)

g(x) = 5x − 4


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

B) The function f(x) has a greater y-intercept.

Explanation:

A) Calculate the slope of f(x) with the following formula:

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

Choose two points and susbtitute them into the formula, then the slope is:

`m=(5-(-7))/(1-(-1))=6`

The equation of the line is:

`y=mx+b`

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

Therefore, the slope of g(x) is:

g(x)=5x-4

m=5

Then the sentence that compares the slopes is: The slope of f(x) is greater than the slope of g(x).

B) As you can see in the equation of the line shown above b is the y-intercept: g(x)=5x-4

Therefore, the y-intercept of g(x) is -4

The slope of f(x) can be determined by remembering that the line intersects the y-axis when x=0.

Then, as you can see in the table, when x=0, y=-1

Therefore the y-intercept of f(x) is -1.

Then, the f(x) has a greater y-intercept.