Question

Razi is filling bags with party favors for his birthday party. The table to the right shows the number of bags he still needs to fill after 4, 5, 6, and 7 minutes. If he is working at a constant rate, what was the initial number of party favor bags Razi had to fill?

Answer 1

The answer is 52.

There's 4 minutes from initially, and a change of 4 per minute. This gives you the 36+16 which is 52.

Answer 2

Answer:

52

Step-by-step explanation:

In this situation, the independent variable (x) is the amount of time in minutes.  The dependent variable (y) is the number of bags remaining.

Since he is working at a constant rate, this makes it a linear function.  In a linear function, the amount he had to fill to begin with is the y-intercept.  Slope-intercept form is y=mx+b, where m is the slope (rate of change) and b is the y-intercept.

However, since we do not have the y-intercept, we will begin instead with point-slope form, y-y₁=m(x-x₁).

Firs twe find the slope using the formula

m = (y₂-y₁)/(x₂-x₁)

m = (32-36)/(5-4) = -4/1 = -4

Using this and the first point, we have

y-36=-4(x-4)

Using the distributive property, we have

y-36 = -4(x)-4(-4)

y-36 = -4x--16

y-36 = -4x+16

Add 36 to each side:

y-36+36 = -4x+16+36

y=-4x+52

This makes the slope -4 and the y-intercept 52; this means he originally had 52 bags to fill.