Question

Determine the slope of the line.

(-4,-4) (-2,-3) (0,-2)

Answer 1

The distance John ran is directly proportional to his time in minutes. Write an equation to model this situation.

Time in minutes (t):
62.5
125
187.5

Distance in miles (d):
5
10
15

Answer 2

To determine the slope of the line, we can use the formula:

slope = (y2 - y1) / (x2 - x1)

Let's calculate the slope using the first two points:

slope1 = (-3 - (-4)) / (-2 - (-4))
= (-3 + 4) / (-2 + 4)
= 1 / 2
= 0.5

Now, let's calculate the slope using the last two points:

slope2 = (-2 - (-3)) / (0 - (-2))
= (-2 + 3) / (0 + 2)
= 1 / 2
= 0.5

Since both calculations result in a slope of 0.5, we can conclude that the slope of the line is 0.5.

Answer 3

To model a situation where the distance John ran is directly proportional to his time in minutes, we can use the equation:

d = kt

where d is the distance in miles, t is the time in minutes, and k is the constant of proportionality.

To find the value of k, we can use one set of data points. Let's use the first data point:

d = 5
t = 62.5

Using these values in the equation, we can solve for k:

5 = k * 62.5

Dividing both sides by 62.5:

k = 5 / 62.5

Simplifying:

k = 0.08

Therefore, the equation to model this situation is:

d = 0.08t