Let's solve the given problem step-by-step to find the equation of the linear function in slope-intercept form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

Step 1: Find the slope ($m$)

The slope is calculated using the formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$

Using two points from the table, say $(1, 9)$ and $(2, 14)$: $m = \frac{14 - 9}{2 - 1} = \frac{5}{1} = 5$

Thus, the slope is $m = 5$.

Step 2: Find the y-intercept ($b$)

We now use the slope-intercept equation $y = mx + b$ and substitute one of the points (e.g., $(1, 9)$) and $m = 5$ to solve for $b$.

$y = mx + b$ $9 = 5(1) + b$ $9 = 5 + b$ $b = 4$

Step 3: Write the equation

Now that we know $m = 5$ and $b = 4$, the equation of the linear function is: $y = 5x + 4$

Would you like further clarification or details about any step? Let me know!

Related Questions:

1. How do you calculate the slope of a line using other points in the table?
2. What is the meaning of the slope in a real-world scenario?
3. How would the graph of $y = 5x + 4$ look? Can we plot it?
4. What happens to the equation if the y-intercept $b$ changes?
5. How can we check if all points in the table lie on the same line?

Tip:

Always use two points to calculate the slope, and verify the consistency of the linear function by checking other points!