A)

Question

The point (12, 9) is included in a direct variation. What is the constant of variation?
(1 point)
1/2
3/4
1
2

Answer 1

To find the constant of variation in the direct variation equation, we can use the formula y = kx, where y and x are the coordinates of a point on the graph, and k is the constant of variation.

In this case, the point (12, 9) is given, which means that 9 is the value of y and 12 is the value of x.

Using the formula, we can substitute these values in to solve for k:

9 = k(12)

To isolate k, we divide both sides of the equation by 12:

9/12 = k

Simplifying, we get:

3/4 = k

Therefore, the constant of variation is 3/4.

Answer 2

A)
The distance d a train travels varies directly with the amount of time t that has elapsed since
departure. If the train travels 475 miles in 9.5 hours, how many miles did the train travel after
4 hours?
(1 point)
100
200
232.5
300

Answer 3

To solve this problem, we can use the formula for direct variation, which states that the distance (d) is equal to the constant of variation (k) multiplied by the time (t).

In this case, we know that the train travels 475 miles in 9.5 hours. This gives us the following equation:

475 = k * 9.5

To find the constant of variation, we divide both sides of the equation by 9.5:

475/9.5 = k

Simplifying, we get:

k = 50

Now, to find the distance the train travels after 4 hours, we substitute the time (t) into the formula and solve for d:

d = k * t
d = 50 * 4
d = 200

Therefore, the train travels 200 miles after 4 hours.