Question

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

x f(x)
−1 −6
0 −3
1 0
g(x)

g(x) = 4x − 5


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.

Answer 1

(A)

Slope for f(x) is 3

Slope for g(x) is 4

(B)

So, y-intercept for f(x) is greater

Explanation:

(A)

Slope of f(x):

we can select any two points

(-1,-6)

so, x1=-1 and y1=-6

(0,-3)

so, x2=0 , y2=-3

now, we can use slope formula

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

now, we can plug values

`m=(-3+6)/(0+1)`

`m=3`

Slope of g(x):

we can compare with

y=mx+b

`g(x)=4x-5`

so, m=4

so, slope is 4

(B)

For f(x):

we can select point as

x=0 , y=-3

so, y-intercept is -3

For g(x):

`g(x)=4x-5`

we can compare with

y=mx+b

where

b is y-intercept

we get

b=-5

we know that -3 is greater than -5

So, y-intercept for f(x) is greater