MHB Quit Ratio - Function Question

[cgr4]

So here's the question.

In industry, the relationship between wages and the quit ratio of employees is defined to be the percentage of employees that quit within 1 year of employment. The quit ratio of a large restaurant chain that pays its employees the minimum wage \$6.55 per hour was .2 or 20 employees per 100. When the company raised the hourly wage to \$8, the quit ratio dropped to .18, or 18 employees per 100.

a) Assuming a linear relationship between the quit ratio Q(x) and the hourly wage x, find an expression for Q(x).

b) What should the hourly wage be for the quit ratio to drop to 10 employees per 100?

So for A.

y₂-y₁ / x₂-₁

Step 1, find the slope?

.18 minus .20 divided by 8 minus 6.55

So the slope would be -.02 / 1.45

 

[MarkFL]

a) $Q$ is the dependent variable and $x$ is the independent variable, and so the slope $m$ of the linear function would be given by:

$$m=\frac{\Delta Q}{\Delta x}=-\frac{2}{145}$$

This agrees with your result, I have just written it as the ratio of one integer to another, as is more traditional for rational numbers.

So, you have the slope, and you have two points to choose from to use in the point-slope formula. What does this give you?