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To find the equation of the line in slope-intercept form (which is \( y = mx + b \)), we need two things:

1. The **slope** (\(m\)): This can be calculated using two points on the line.
2. The **y-intercept** (\(b\)): This is the value of \(y\) when \(x = 0\).

### Step 1: Identify two points on the line
From the graph:
- The line passes through the points \((-6, 0)\) and \((0, 3)\).

### Step 2: Calculate the slope (\(m\))
The formula for the slope is:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Using the points \((-6, 0)\) and \((0, 3)\):
\[
m = \frac{3 - 0}{0 - (-6)} = \frac{3}{6} = \frac{1}{2}
\]

### Step 3: Identify the y-intercept (\(b\))
The y-intercept is the point where the line crosses the y-axis. From the graph, this happens at \(y = 3\). So, \(b = 3\).

### Step 4: Write the equation
Now that we have the slope \(m = \frac{1}{2}\) and the y-intercept \(b = 3\), the equation of the line in slope-intercept form is:

\[
y = \frac{1}{2}x + 3
\]

Would you like more details on any of the steps, or do you have any questions?

### Related Questions:
1. How do you find the slope of a line given two points?
2. What is the significance of the y-intercept in the slope-intercept form?
3. How do you determine if two lines are parallel by comparing their slopes?
4. What are alternative forms of a line equation besides slope-intercept?
5. How can you find the equation of a line if you're given its slope and one point on it?

### Tip:
To quickly check if your slope is correct, remember that "rise over run" is a visual way to calculate it directly from the graph by counting vertical and horizontal units between two points!

What is the equation of the line in slope-intercept form?

Learn how to find the equation of a line in slope-intercept form with this detailed step-by-step solution. The problem involves calculating the slope and identifying the y-intercept using points from a graph. Ideal for students in Grades 7-9.

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