Question

A table contains the ordered pairs (3, 42.25) and (5, 50.75). If the relationship in the table is linear, explain how to find the initial value.

Answer 1

Answer:

Find the constant change first. Then subtract the constant chane from the output until the imput is 0.

Step-by-step explanation:

Answer 2

Answer:

The initial value is 29.5

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

b is the y-intercept ( also called initial value)

we have the points

(3,42.25) and (5,50.75)

Find the slope m

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

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

substitute the values

$m=\frac{50.75-42.25}{5-3}$

$m=\frac{8.5}{2}$

$m=4.25$

substitute in the equation

$y=4.25x+b$

Find the value of b

with the point (3,42.25)  ( or the other given point)

substitute the value of x and the value of y in the equation and solve for b

$42.25=4.25(3)+b$

$42.25=12.75+b$

$b=42.25-12.75$

$b=29.5$

substitute

The linear equation is

$y=4.25x+29.5$

The initial value is the y-intercept (value of y when the value of x is equal to zero)

For x=0

$y=4.25(0)+29.5$

$y=29.5$

Therefore

The initial value is 29.5