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.

The initial value is 29.5

Step-by-step explanation:

we know that

The linear equation in slope intercept form is equal to

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

substitute the values

substitute in the equation

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

substitute

The linear equation is

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

For x=0

Therefore

The initial value is 29.5