Question

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

x f(x)
−1 −11
0 −1
1 9
g(x)

g(x) = 5x + 1



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

Answer: The slope of f(x) is 10 the slope of g(x) is 5. g(x) has a greater y-intercept.

Step-by-step explanation:

From the table it is noticed that the line f(x) passes through the points (-1,-11) and (0,-1).

Slope of the line,

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

`m=(-1-(-11))/(0-(-1)) =(10)/(1)=10`

Therefore the slope of f(x) is 10 and the y intercept is (0,-1).

`y=mx+b`

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

`g(x)=5x+1`

On comparing g(x) with slope intercept form we get,

`m=5,b=1`

Therefore slope of g(x) is 5 and the y intercept is (0,1).

Therefore the slope of f(x) is greater than g(x) and the function g(x) has a greater y-intercept.