Question

Employees at a company make a base salary of $750 each week. Employees who work at least 30 hours per week can make the base salary plus $10 per hour for every hour over 30. Employees are not allowed to exceed more than 40 hours a week. Let x be the number of additional hours each employee works. Then, the function f(x) = 10x + 750 represents their weekly earnings.
Determine the key features based on the function given for the situation.

The equation has a slope of and a y-intercept at (0,__). The equation has an x-intercept at (__,0).

Answer 1

Slope = 10

y intercept at (0,750)

x intercept at (-75, 0)

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Explanation:

The function f(x) = 10x+750 is the same as y = 10x+750

It is in the form y = mx+b where m = 10 is the slope and b = 750 is the y intercept. So that covers the first two parts of the answer.

The x intercept is found by replacing y with 0, then solving for x like shown below

y = 10x + 750

0 = 10x + 750

10x + 750 = 0

10x = -750 ....... subtract 750 from both sides

x = -750/10 .... divide both sides by 10

x = -75

So x = -75 plugged into the function leads to y = 0

Meaning that x = -75 and y = 0 pair up together to get the point (-75,0) which is the x intercept. This is the location where the line crosses the x axis.