To write the equation of the line in slope-intercept form $y = mx + b$, let's analyze the graph shown in your image.

Step 1: Identify two points on the line.

From the graph, it looks like two points the line passes through are:

• $(0, 2)$ (the y-intercept)
• $(2, 5)$

Step 2: Calculate the slope $m$.

The slope formula is: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Using the two points $(0, 2)$ and $(2, 5)$: $m = \frac{5 - 2}{2 - 0} = \frac{3}{2}$

Step 3: Write the equation in slope-intercept form.

We know the slope $m = \frac{3}{2}$ and the y-intercept $b = 2$ (since the line crosses the y-axis at $y = 2$).

Thus, the equation of the line is: $y = \frac{3}{2}x + 2$

This is the slope-intercept form of the equation for the given line.

Let me know if you have any questions! Here are a few related questions:

1. How do you find the slope if the points are negative?
2. What if the y-intercept is a fraction?
3. How do you convert slope-intercept form to standard form?
4. What is the significance of slope in real-world contexts?
5. How would the equation change if the line had a negative slope?

Tip: Always double-check your points and slope calculations to avoid sign errors.