Question

Function 1 is represented by the equation, y = 0.75x - 1. Function 2 is represented by the graph below. Which about the function is true?

1- function 1 has the greater rate of change but function 2 has the greater y-intercept

2-Function 1 has the greater rate of change and greater y-intercept

3-Function 2 has the greater rate of change and the greater y intercept

4-Fuction 2 has the greater rate of change but function 1 has the greater y-intercept​

Answer 1

Answer: 1- function 1 has the greater rate of change but function 2 has the greater y-intercept

Explanation:

We know that function 1 is:

y = f₁(x) = 0.75*x - 1

And for the second linear equation we can see that it passes through the points (-3, -1) and (0,1)

Then the slope is:

a = (1 - (-1))/(0 - (-3)) = 2/3

then the equation is something like:

y = f₂(x) = (2/3)*x + b

To find the value of b, we use the fact that when x = 0, we have y = 1.

Then:

1 = (2/3)*0 + b

1 = b

Then the equation for function 2 is:

f₂(x) = (2/3)*x + 1

So the two equations are:

f₁(x) = 0.75*x - 1

f₂(x) = (2/3)*x + 1

Where we can see that function 1 has a greater slope (rate of change) and function two has a greater y-intercept.

Then the correct option is

(1- function 1 has the greater rate of change but function 2 has the greater y-intercept)