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

Step 1: Identify two points on the line

From the graph, two points on the line are:

• Point 1: $(-8, -8)$
• Point 2: $(0, -4)$

Step 2: Calculate the slope ($m$)

The slope formula is: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Substitute the coordinates of the two points: $m = \frac{-4 - (-8)}{0 - (-8)} = \frac{-4 + 8}{8} = \frac{4}{8} = \frac{1}{2}$

Thus, the slope is $m = \frac{1}{2}$.

Step 3: Determine the $y$-intercept ($b$)

The $y$-intercept is the value of $y$ when $x = 0$. From the graph, the line crosses the $y$-axis at $(0, -4)$, so $b = -4$.

Step 4: Write the equation of the line

The equation of the line is: $y = \frac{1}{2}x - 4$

Final Answer:

$y = \frac{1}{2}x - 4$

Let me know if you'd like a deeper explanation or further help!

Follow-up Questions:

1. What is the general form of a linear equation, and how is it related to slope-intercept form?
2. How do you calculate the slope if the points are not obvious from the graph?
3. Why is it important to simplify fractions when writing equations?
4. What changes in the equation if the slope is negative?
5. Can you derive the equation of a vertical or horizontal line from a graph?

Tip:

When identifying points on a line from a graph, try to pick points where the line crosses grid intersections to avoid estimation errors!