To determine the equation of the line in slope-intercept form ($y = mx + b$) from the graph, we need to identify both the slope ($m$) and the y-intercept ($b$).

Step 1: Find the slope ($m$)

The slope is calculated as the rise over the run:

$m = \frac{\text{change in } y}{\text{change in } x}$

From the graph, we can observe two points the line passes through:

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

Using these points, calculate the slope:

$m = \frac{2 - (-3)}{3 - 1} = \frac{5}{2}$

So, the slope is $\frac{5}{2}$.

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

The y-intercept ($b$) is where the line crosses the y-axis. Looking at the graph, the line crosses the y-axis at $(0, -5.5)$. Therefore, the y-intercept is $b = -\frac{11}{2}$.

Final equation

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

$y = \frac{5}{2}x - \frac{11}{2}$

Would you like further details on any step, or do you have other questions?

Here are 5 related questions:

1. How can I find the slope if the graph is not clear?
2. What are other forms of linear equations besides slope-intercept form?
3. How do you calculate the y-intercept if the graph is missing?
4. Can the slope be negative? What does it represent?
5. How do I graph a line from its equation?

Tip: When working with fractions in slope-intercept form, simplify them where possible to avoid errors in interpretation.