Question

A relation is plotted as a linear function on the coordinate plane starting at point A (0, 3) and

ending at point B (2,7)
What is the rate of change for the linear function and what is its initial value?
Select from the drop-down menus to correctly complete the statements.
The rate of change is Choose..._____
and the initial value is Choose_____

Answer 1

The rate of change is 2 and the initial value is 3.

Explanation:

took the unit test

Answer 2

Part 1) The rate of change is 2

Part 2) The initial value is 3

Explanation:

we know that

The linear equation in slope intercept form is equal to

`y=mx+b`

where

m is the slope or unit rate of the linear equation

b is the y-intercept

Remember that in a linear equation the rate of change is a constant and is equal to the slope and the initial value is equal to the y-intercept (value of y when the value of x is equal to zero)

step 1

Find the slope

we have the coordinates

A(0,3) and B(2,7)

The formula to calculate the slope between two points is equal to

`m=(y2-y1)/(x2-x1)`

substitute in the formula

`m=(7-3)/(2-0)`

`m=(4)/(2)=2`

therefore

The rate of change is 2

step 2

Find the y-intercept or initial value

Remember that the y-intercept is the value of y when the value of x is equal to zero

In this problem the y-intercept is given

The y-intercept is the point A(0,3)

so

`b=3`

therefore

The initial value is 3