Question

Two linear functions are represented in different formats.

Function 1:

x y
0 −2
2 0
3 1
5 3
Function 2:

Graph of a line passing through the point begin ordered pair negative 2 comma 0 end ordered pair and the point begin ordered pair 0 comma 4 end ordered pair.

Which statements are true?

Select each correct answer.


Function 1 has a greater rate of change than function 2.

Function 2 has a greater rate of change than function 1.

Function 1 has a greater y-intercept than function 2.

Function 2 has a greater y-intercept than function 1.

Answer 1

The statements that are true are;

Function 2 has a greater rate of change than function 1.

Function 2 has a greater y-intercept than function 1.

Explanation:

Given that function 1 has the table;

x y

0 -2

2 0

3 1

5 3

Finding the slope of the linear function gives the rate of change of the function. In this case,

m=Δy/Δx

m=3-1/5-3 = 2/2 =1

The equation of the linear function is given as;

m=Δy/Δx

y-3/x-5= 1

y-3=x-5

y=x-5+3

y=x-2

y-intercept is -2

In function 2, the line passes through points (-2,0) and (0,4)

Finding the slope of the line,

m₁=Δy/Δx

m₁=4-0/0--2

m₁= 4/2 =2

Rate of change is 2

Finding the equation of the line

y-4/x-0 = 2

y-4=2(x-0)

y-4 =2x

y=2x+4

The y-intercept is 4

The statements that are true are;

Function 2 has a greater rate of change than function 1.

Function 2 has a greater y-intercept than function 1.