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 linear relationship ( the linear equation ):
y = m x + b ( the slope-intercept form )
m = ( 50.75 - 42.25 ) / ( 5 - 3 ) = 8.50 / 2 = 4.25 ( the slope )
42.25 = 4.25 * 3 + b
b = 42.25 - 12.75
b = 29.50
y = 4.25 * x + 29.50
Answer:
The initial value is : ( 0, 29.50 ) or 29.50.

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ahirohit963 ahirohit963 · Answer 2 · 2021-11-09T07:29:59+01:00

If the relationship in the table is linear, then the initial value will be (0,29.5) and this can be determine by using the point slope form of the linear equation.

Given :

A table contains the ordered pairs (3, 42.25) and (5, 50.75).
The relationship in the table is linear.

To determine the initial value of the table, first determine the linear equation by using the point slope form of the linear equation, that is:

[tex]\dfrac{y-y_1}{x-x_1}=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

Now, put the values of [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] in the above equation.

[tex]\dfrac{y-42.25}{x-3}= \dfrac{50.75-42.25}{5-3}[/tex]

[tex](y-42.25)= \dfrac{8.5}{2}(x-3)[/tex]

[tex]y-42.25=4.25(x-3)[/tex]

[tex]y-42.25=4.25x-12.75[/tex]

[tex]y = 4.25x+29.5[/tex] --- (1)

Now, put x = 0 in equation (1) to determine the initial value.

[tex]y = 4.25\times 0 +29.5[/tex]

y = 29.5

Therefore, if the relationship in the table is linear, then the initial value will be (0,29.5).

For more information, refer the link given below:

https://brainly.com/question/19881501