Question

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

Answer 1

Answer:

Part 1) The rate of change is $\frac{1}{3}$

Part 2) The initial value is $12$

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

(3,13) and (6,14)

substitute the values in the formula

$m=\frac{14-13}{6-3}$

$m=\frac{1}{3}$

therefore

The rate of change is $\frac{1}{3}$

step 2

Find the initial value

we have

$m=\frac{1}{3}$

$point\ (3,13)$

substitute in the equation $y=mx+b$

$13=\frac{1}{3}(3)+b$

solve for b

$13=1+b$

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

The linear equation is equal to

$y=\frac{1}{3}x+12$

The y-intercept or initial value is 12