Question

(5,12)and (2,6) rate of change? Initial value? HURRY i NEED this done.

Answer 1

Answer:

Part 1) The rate of change is $2$

Part 2) The initial value is $2$

Step-by-step 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

$m=\frac{y2-y1}{x2-x1}$

we have the points

(5,12)and (2,6)

substitute the values in the formula

$m=\frac{6-12}{2-5}$

$m=\frac{-6}{-3}$

$m=2$

therefore

The rate of change is $2$

step 2

Find the initial value

we have

$m=2$

$point\ (2,6)$

substitute in the equation $y=mx+b$

$6=2(2)+b$

solve for b

$6=4+b$

$b=2$ ---> initial value

The linear equation is equal to

$y=2x+2$

The y-intercept or initial value is 2