Question

Write and equation in slope intercept form to model the situation.

A candle is 8 inches tall and burns at 3/4 inch each hour.

Answer 1

The equation that models the situation is
`y = 8 - 0.75t`

Explanation:

Equation of a line:

The equation of a line, in slope-intercept formula, has the following format:

`y = mx + b`

In which m is the slope(how much y changes when x changes by 1 unit) and b is the intercept, which is the value of t when x = 0.

A candle is 8 inches tall and burns at 3/4 inch each hour.

Using t as number of hours and y as the height.

Initial height of 8 inches, that is, when
`t = 0, y = 8`, so
`b = 8`

Burns at 3/4 inch each hour.

That is, the height decreases by a rate of 3/4 inch each hour, so
`m = -(3)/(4) = -0.75`

So

`y = 8 - 0.75t`