To solve this problem, we need to determine the linear function that represents Jack's pay based on the hours he works, as shown in the table. Since it's linear, the general form of the equation should be:

$f(x) = mx + b$

where:

• $m$ is the hourly wage (slope),
• $b$ is the set amount he earns regardless of hours (y-intercept).

Step 1: Determine the Slope ($m$)

We can calculate $m$ by taking the difference in pay and dividing it by the difference in hours between two points. Let’s use the data points $(1, 18)$ and $(3, 38)$.

$m = \frac{38 - 18}{3 - 1} = \frac{20}{2} = 10$

So, Jack’s hourly wage $m$ is 10.

Step 2: Determine the Y-intercept ($b$)

Using the slope $m = 10$, we can substitute one of the points to solve for $b$. Let’s use the point $(1, 18)$.

$18 = 10(1) + b$ $18 = 10 + b$ $b = 8$

So, the y-intercept $b$ is 8.

Step 3: Write the Equation

The linear function for Jack’s pay is:

$f(x) = 10x + 8$

Answer

The correct option is: $f(x) = 10x + 8$

Would you like further details or have any questions?

Here are 5 related questions that build on this problem:

1. How would the equation change if Jack’s hourly wage increased?
2. What would Jack’s pay be if he worked 4 hours?
3. How can you determine if a relationship is linear just by looking at a table of values?
4. How would you solve if you only had one point and the slope?
5. What does the y-intercept represent in real-life contexts?

Tip: When determining a linear relationship, calculating the slope between multiple points helps confirm consistency in rate of change.