To find the equation of the linear function from the table, we can use the slope-intercept form, which is:

$y = mx + b$

Where:

• $m$ is the slope of the line,
• $b$ is the y-intercept.

Step 1: Calculate the slope ($m$)

The slope of a line is given by:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

We can pick any two points from the table to calculate the slope. Let’s choose the points $(x_1, y_1) = (-1, -6)$ and $(x_2, y_2) = (1, 4)$.

$m = \frac{4 - (-6)}{1 - (-1)} = \frac{4 + 6}{1 + 1} = \frac{10}{2} = 5$

So, the slope $m = 5$.

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

Now that we have the slope, we can substitute $m = 5$ and any point from the table into the slope-intercept form to find $b$. Let's use the point $(1, 4)$.

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

Step 3: Write the equation

The equation of the line is:

$y = 5x - 1$

This is the equation of the linear function in slope-intercept form.

Let me know if you need more details, or if you'd like help with further problems!

Here are 5 related questions to explore further:

1. How do you find the slope if given only one point and the equation of a line?
2. Can you find the equation of a line if you know the slope and one point?
3. How would the equation change if the slope were negative?
4. What is the geometric interpretation of the y-intercept on a graph?
5. How do you convert the equation from slope-intercept form to standard form?

Tip: Always check your slope using two different pairs of points to ensure consistency in calculations.