Question

Benjamin is going to drive from his house to City A without stopping. An equation that determines Benjamin's distance from City A tt hours after leaving his house is D=260-65t.D=260−65t. What is the slope of the equation and what is its interpretation in the context of the problem?

Answer 1

The slope of the function is -65 which reveals the average speed that Benjamin travels, in miles per hour.

Explanation:

The slope shows how much the distance to City A decreases each hour, implying that Benjamin is driving an average speed of 65 miles per hour.

Have a good day :)

Answer 2

Given:

The Benjamin's distance from City A, t hours after leaving his house is

`D=260-65t`

To find:

The slope of the equation and what is its interpretation in the context of the problem?

Solution:

The slope intercept form of a line is

`y=mx+b`

where, m (coefficient of variable x) is slope and b is y-intercept.

We have, the equation

`D=260-65t`

It is a linear equation and the coefficient of variable t is -65. So, the slope of the equation -65.

It means, the Benjamin's distance from City A is decreases at the rate of 65 units per hour or we can say the speed of Benjamin is 65 units per hour.

Therefore, slope of the equation -65. It means, Benjamin's distance from City A is decreases at the rate of 65 units per hour.