Question

Cans of paint weigh 6 pounds each. Let x represent the number of cans of paint and y represent the total weight of the cans. Write the equation to this situation as slope intercept form (y=mx+b). Then create a table of possible values

Answer 1

The equation for the relationship between the number of cans of paint, x, and the total weight of the cans, y, in slope-intercept form is y = 6x + 0. This equation can be derived from the formula for the slope-intercept form of a line, y = mx + b, where m is the slope of the line and b is the y-intercept. In this case, since the weight of each can of paint is 6 pounds and there is no y-intercept (the line passes through the origin), the slope of the line is 6 and the y-intercept is 0.

A table of possible values for the number of cans of paint, x, and the total weight of the cans, y, based on this equation is shown below:

x (number of cans of paint) y (total weight of cans)

1 6

2 12

3 18

4 24

5 30

As the table shows, for each additional can of paint, the total weight of the cans increases by 6 pounds. This is because each can of paint weighs 6 pounds, and the weight of the cans is equal to the number of cans multiplied by the weight of each can.

Answer 2

Answer: y = 6x

Explanation:

For each can of paint (x) 6 pounds is added. This is represented as;

y = 6x

For the table of possible values, we will plug a value in for x, and then evaluate the function for y. See attached.

y = 6(1) = 6

y = 6(2) = 12

y = 6(3) = 18