Question

On a trip to Orlando, FL the Holden Family had traveled 130 miles in 2 hours. Three hours later they had traveled 310 miles. Two hours later they had traveled 430 miles. Since they maintained a constant speed there trip so far represents a linear function. Fill in the blanks on the table below to chart their trip.

Answer 1

Answer:

The table is not shown, so i will answer this in a general way.

We know that the speed is constant, then we can model the relation between the distance and the time with a linear relationship.

A linear relationship can be written as:

y = a*x + b

where a is the slope and b is the y-axis intercept.

For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:

a = (y2 - y1)/(x2 - x1).

In this case, we have the points:

the Holden Family had traveled 130 miles in 2 hours.

(2h, 130mi)

Three hours later they had traveled 310 miles.

(5h, 310mi)

Two hours later they had traveled 430 miles.

(7h, 430mi)

We can calculate the slope with two different points, and see if it coincides.

a = (430mi - 130mi)/(7h - 2h) = (300mi)/5h = 60mi/h

Now let's try with other two points:

a = (430mi - 310mi)/(7h - 5h) = 120mi/2h = 60mi/h

Then the slope (that is the speed) is 60mi/h.

Then the movement equation is:

y = 60mi/h*x + b

To find the value of b, we can just replace one of the points in the equation, let's replace the point (2h, 130mi)

130mi = 60mi/h*2h + b

130mi = 120mi + b

130mi - 120mi = b

10mi = b

Then the movement equation is:

y = 60mi/h*x + 10mi