To find the equation of the linear function from the given table, we need to write the equation in slope-intercept form, which is:

$y = mx + b$

Where:

• $m$ is the slope of the line.
• $b$ is the y-intercept (the value of $y$ when $x = 0$).

Step 1: Find the slope ($m$)

The slope $m$ is the rate of change of $y$ with respect to $x$, which can be calculated as:

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

From the table, pick any two points. Let's take the points $(x_1, y_1) = (0, -4)$ and $(x_2, y_2) = (1, 2)$.

$m = \frac{{2 - (-4)}}{{1 - 0}} = \frac{2 + 4}{1} = \frac{6}{1} = 6$

So, the slope $m = 6$.

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

From the table, we can see that when $x = 0$, $y = -4$. Therefore, the y-intercept $b = -4$.

Final Equation

Now that we know the slope and the y-intercept, the equation of the line is:

$y = 6x - 4$

You can now enter this as the equation for the linear function.

Do you need further clarification or details? Here are some related questions:

1. What is the general form of a linear equation?
2. How can you determine the slope of a line from a table?
3. What does the y-intercept represent in a real-world context?
4. How do you verify if a table represents a linear function?
5. Can we derive a linear equation using different pairs of points?

Tip: Always choose two clear points from the table to calculate the slope accurately.