Question

Tools Question 2 Nicolas makes toys at a toy shop. The graph represents the relationship between the number of toys (1) that Nicolas makes and the number of hours Toy Making 50 45 40 35 30 Number of Toys 25 20 15 10 2 6 10 Number of Hours Which of the following equations represents a toy-making rate, in toys per hour, that is HALF that of Nicolas's toy-making rate?

Answer 1

The equation of a proportional relationship between two variables x and y with a constant of proportionality k, is:

`y=kx`

If y represents the number of toys and x represents the number of hours, substitute the corresponding values of x and y to find the constant of proportionality k. Use, for instance, the fact that Nicholas made 40 toys in 10 hours:

`40=k\cdot10`

Divide both sides of the equation by 10:

`k=4`

Since Nicholas's toy-making rate is 4 toys per hour, half that rate would be 2 toys per hour. Then, out equation would become:

`y=2x`

Using the letter "t" for toys instead of y and "h" for hours instead of x, then:

`t=2h`