We are tasked with finding the equation of the line in slope-intercept form based on the given table of values.

The slope-intercept form is:

$y = mx + b$

where $m$ is the slope, and $b$ is the y-intercept.

Step 1: Calculate the Slope ($m$)

The slope $m$ can be calculated using the formula:

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

We can pick any two points from the table. Let’s use the points $(-6, 10)$ and $(0, 0)$:

$m = \frac{{0 - 10}}{{0 - (-6)}} = \frac{{-10}}{{6}} = -\frac{5}{3}$

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

The y-intercept $b$ is the value of $y$ when $x = 0$. From the table, we can see that when $x = 0$, $y = 0$. So, $b = 0$.

Step 3: Write the Equation

Now that we have the slope $m = -\frac{5}{3}$ and the y-intercept $b = 0$, the equation of the line is:

$y = -\frac{5}{3}x$

Would you like further clarification or details on any part of the process? Here are some related questions:

1. How do you interpret the slope geometrically?
2. What happens if the y-intercept is not zero?
3. How can you verify the equation using another pair of points?
4. How does the slope affect the steepness of the line?
5. What is the difference between slope-intercept form and point-slope form?

Tip: Always double-check your calculations by verifying the equation with other points in the table!