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

29.5

Explanation:

If the relationship is linear, we can find the constant ratio of change with the given points.

`m=(50.75-42.25)/(5-3)=(8.5)/(2) =4.25`

Then, we use the point-slope formula to find the equation, which is gonna give us the initial value (constant term of the equation).

`y-y_(1) =m(x-x_(1) )\\y-42.25=4.25(x-3)\\y=4.25x-12.75+42.25\\y=4.25x+29.5`

Therefore, the initial value is 29.5.

Remember that the constant term in the linear equation refes to the initial value of a problem. So, the plan is to find the equation to know the initial value.

Answer 2

(0, 29.50)

Explanation:

y increases 8.50 units for every 2 units that x increases, or

y increases 4.25 units per unit of x.

For the same reason, if we decrease x from 3 to 0 (3 units),

y decreases by 3 × 4.25 units = 12.75 units.

y = 42.25 - 12.75 = 29.50

The initial value is at (0, 29.50).

The graph below shows your two points and the line joining them extrapolated back to the initial value at (0, 29.50).