Question

(3,13) and (6,14)
Rate of change and initial value???
Please help me

Answer 1

Part 1) The rate of change is
`(1)/(3)`

Part 2) The initial value is
`12`

Explanation:

we know that

The linear equation in slope intercept form is equal to

`y=mx+b`

where

m is the slope or rate of change

b is the y-intercept or initial value

step 1

Find the slope or rate of change

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

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

we have the points

(3,13) and (6,14)

substitute the values in the formula

`m=(14-13)/(6-3)`

`m=(1)/(3)`

therefore

The rate of change is
`(1)/(3)`

step 2

Find the initial value

we have

`m=(1)/(3)`

`point\ (3,13)`

substitute in the equation
`y=mx+b`

`13=(1)/(3)(3)+b`

solve for b

`13=1+b`

`b=13-1=12` ---> initial value

The linear equation is equal to

`y=(1)/(3)x+12`

The y-intercept or initial value is 12