Question

The data in the table below represents a linear relationship.

Based on the table of values, which equation can be used to describe the relationship between x and y?

Answer 1

`y = -3,000x + 15,000`

Step-by-step explanation:

A linear relationship is usually represented by the equation,
`y = mx + b`, where m = slope, and b = y-intercept.

Find m and b to derive an equation that describes the relationship between x and y.

Hours since 4 p.m is the x-variable and number of tickets remaining is the y-variable.

Using two coordinate pairs, (3, 6,000) and (4, 3,000), find the slope (m):

`slope(m) = (y_2 - y_1)/(x_2 - x_1) = (6,000 - 3,000)/(3 - 4) = (3,000)/(-1)`

Slope (m) = -3,000

Substitute x = 5, y = 0, and m = -3,000 into
`y = mx + b`, to find the value of b. (Note that you can the value of any coordinate pair as x and y. You'd get the same value of b)

`0 = (-3,000)(5) + b`

`0 = -15,000 + b`

Add 15,000 to both sides

`15,000 = b`

`b = 15,000`

Substitute b = 15,000 and m = -3,000 into
`y = mx + b`, to get the equation that describes the relationship between x and y.

`y = -3,000x + 15,000`