Greg car travels 13 feet per second. after 2 seconds his car was 30.7 feet from the start line . when then time started marti's cad was 2 feet in front of the start line . her car travels 16.5 feet per second . write an equation that represents the relationship between the time and distance

The linear model of Greg's car is given by:

The linear model of Marti's car is given by:

Step-by-step explanation:

Let:

represent distance traveled by the cars in feet.

represent time of travel in seconds.

Greg's Car:

Given:

Rate of change = 13 ft/s

After 2 seconds his car was 30.7 feet.

From the given data we have the following:

Slope of line = 13 ft/s

Point

Using point slope equation to model the linear relationship.

where is a point on line.

So, we have:

   [ Using distribution.]

Adding 30.7 to both sides.

The linear model of Greg's car is given by:

Marti's car:

Given:

Rate of change = 16.5 ft/s

Starting point = 2 ft

From the given data we have the following:

Slope of line = 16.5 ft/s

y-intercept = 2 ft

Using slope intercept equation to model the linear relationship.

where is slope of line or rate of change and is the y-intercept or stating point.

So, we have:

The linear model of Marti's car is given by: