To find the equation of the line in slope-intercept form, $y = mx + b$, we need two pieces of information from the graph:

1. The slope $m$ of the line.
2. The y-intercept $b$ (where the line crosses the y-axis).

Step 1: Determine the Slope $m$

The slope of a line is calculated by using two points on the line, using the formula: $m = \frac{{y_2 - y_1}}{{x_2 - x_1}}$

From the graph, let's pick two points on the line:

• Point 1: $(-9, 9)$
• Point 2: $(3, 0)$

Now calculate the slope: $m = \frac{{0 - 9}}{{3 + 9}} = \frac{{-9}}{{12}} = -\frac{3}{4}$

So, the slope $m = -\frac{3}{4}$.

Step 2: Determine the y-intercept $b$

The y-intercept is where the line crosses the y-axis. From the graph, we can observe that the line crosses the y-axis at $y = 6$. Therefore, $b = 6$.

Final Equation

Now that we have both $m$ and $b$, we can write the equation of the line in slope-intercept form: $y = -\frac{3}{4}x + 6$

This is the equation of the line in fully simplified slope-intercept form.

Would you like further details on how to interpret slope and y-intercepts on graphs, or have any other questions?

Here are five related questions for practice:

1. How would the equation change if the y-intercept were different?
2. What is the significance of a negative slope on a graph?
3. How would the line appear if the slope were positive instead of negative?
4. How can you verify the equation of a line using other points on the graph?
5. What happens to the line if we change the slope but keep the same y-intercept?

Tip: When finding the slope from two points, make sure to keep track of the signs in the subtraction to avoid errors.