To find the equation of the line in slope-intercept form, $y = mx + b$, we need to determine the slope $m$ and the y-intercept $b$ of the line.

Step 1: Find the y-intercept $b$

From the graph, the line crosses the y-axis at $y = -2$. Therefore, the y-intercept $b = -2$.

Step 2: Find the Slope $m$

The slope $m$ is calculated using the formula: $m = \frac{\text{rise}}{\text{run}}$ Choose two points on the line. From the graph, it appears that the line passes through:

• Point 1: $(-6, -5)$
• Point 2: $(0, -2)$

Using these points: $m = \frac{-2 - (-5)}{0 - (-6)} = \frac{3}{6} = \frac{1}{2}$

Step 3: Write the Equation

With $m = \frac{1}{2}$ and $b = -2$, the equation of the line is: $y = \frac{1}{2}x - 2$

Final Answer

The equation in slope-intercept form is: $y = \frac{1}{2}x - 2$

Would you like a deeper explanation of any part of this solution, or have any questions?

Here are five questions related to this concept:

1. How do you find the slope if you have two points on a line?
2. What does the y-intercept represent in a graph?
3. How can you verify if a line is increasing or decreasing from its slope?
4. What is the significance of the slope in the context of real-world problems?
5. How do you convert slope-intercept form to standard form?

Tip: Always reduce the slope fraction to its simplest form for clarity in answers.