Question

To help the environment and make some extra money, Dale takes his empty cans to the Cash Not Trash recycling shop. The shop pays cash based on the total weight of the cans Dale brings in for recycling.

There is a proportional relationship between the weight (in pounds) of the cans Dale brings into the shop, x, and the amount (in dollars) the shop pays Dale, y.
x (pounds) y (dollars)
6 $3
8 $4
14 $7
16 $8
Write an equation for the relationship between x and y. Simplify any fractions.
y=

Answer 1

To write an equation for the proportional relationship between the weight of cans and the amount of money paid, divide y by x to find the constant ratio. The equation is y = (1/2)x, representing a straight line with a slope of 1/2 and a y-intercept of 0.

Step-by-step explanation:

• To write an equation for the relationship between x and y, we need to identify the pattern in the given data. From the table, we can see that as the weight of the cans increases, the amount of money paid also increases.
• The relationship between x (pounds) and y (dollars) is proportional, which means that the ratio of y to x is constant. To find this ratio, we can take any pair of x and y values and divide y by x.
• For example, let's use the first pair of values: 6 pounds and $3. The ratio of y to x is 3/6 = 1/2. We can confirm that this ratio holds true for all the other pairs of values as well.
• Therefore, the equation for the relationship between x and y is y = (1/2)x. This equation represents a straight line with a slope of 1/2 and a y-intercept of 0, since when x is 0, y is also 0.