Question

This is due today i would appreciate it a lot if smn could help me with it :/

Answer 1

Conclusion:

The rate of change of function 1 = 3

The rate of change of function 2 = 5/3

• Hence, function 1 has a greater rate of change

The initial Value of function 1 = y = 2

The initial Value of function 2 = y = 3

• Hence, function 2 has a greater initial value.

Explanation:

Function 1)

Determining rate of change for function 1:

x 1 2 3 4

y 5 8 11 14

Finding the rate of change or slope using the formula

Rate of change = m = [y₂-y₁] / [x₂-x₁]

Taking any two points, let say (1, 5) and (2, 8)

Rate of change = m = [8-5] / [2-1]

= 3/1

= 3

Therefor, the rate of change of function 1 = m = 3

using point-slope form to determine the function equation

y-y₁ = m (x-x₁)

where m is the rate of change or slope

substititng m = 3 and the point (1, 5)

y - 5 = 3(x - 1)

y - 5 = 3x-3

y = 3x-3+5

y = 3x + 2

Thus, equation of function 1 will be:

y = 3x + 2

Determining Initial Value for Function 1:

substituting x = 0 in the equation to determine the initial value

y = 3(0)+2

y = 0+2

y = 2

Therefore, the initial Value of function 1 will be: y = 2

Function 2)

Determining the rate of change for function 2:

Given the function 2

`y\:=\:(5)/(3)x+3`

comparing with the slope-intercept form of a linear function

y = mx+b where m is the rate of change

so the rate of change of function 2 = m = 5/3

Determining Initial Value for Function 2:

substituting x = 0 in the equation to determine the initial value

`y\:=\:(5)/(3)x+3`

`y\:=\:(5)/(3)\left(0\right)+3`

`y = 0+3`

`y = 3`

Therefore, the initial Value of function 2 will be: y = 3

Conclusion:

The rate of change of function 1 = 3

The rate of change of function 2 = 5/3

• Hence, function 1 has a greater rate of change

The initial Value of function 1 = y = 2

The initial Value of function 2 = y = 3

• Hence, function 2 has a greater initial value.