Question

There are 48 inches in 4 feet, which is represented by the equation 4y=48x . Determine the number of inches per foot.(1 point)

Answer 1

The graph shows the proportional relationship. Derive the equation of the line y=mx through the origin. (1 point)

Answer 2

The number of ushers at a basketball game is directly proportional to the number of spectators. If there are 510 spectators at the game, 17 ushers are needed. How many ushers are needed if there are 1,050 spectators?(1 point)

Answer 3

To find the number of inches per foot, we can rewrite the equation as:

4y = 48x

Dividing both sides by 4 gives:

y = 12x

This means that for every 1 foot (x), there are 12 inches (y). Therefore, there are 12 inches per foot.

Answer 4

If the graph shows a proportional relationship and passes through the origin, then the equation of the line will be of the form y = mx, where m is the slope of the line.

To determine the slope (m), we can use any two points on the line. Since the line passes through the origin, one point we can use is (0,0) and another point might be (x, y).

Slope (m) is calculated as:

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

Using the points (0,0) and (x, y), we have:

m = (y - 0) / (x - 0)
m = y / x

Therefore, the equation of the line y = mx through the origin is simply y = x.

Answer 5

Since the number of ushers is directly proportional to the number of spectators, we can set up a proportion using the information given.

Let x be the number of ushers needed if there are 1,050 spectators.

We can set up the proportion as follows:

510 spectators / 17 ushers = 1,050 spectators / x ushers

Solve for x:

(510 * x) = (17 * 1,050)
510x = 17,850
x = 17,850 / 510
x = 35

Therefore, if there are 1,050 spectators at the game, 35 ushers would be needed.