To determine the equation of the line shown on the graph in slope-intercept form $y = mx + b$, we need to find two things:

1. The slope $m$ of the line.
2. The y-intercept $b$ (where the line crosses the y-axis).

Step 1: Determine the slope $m$

The slope $m$ is the "rise over run," meaning the change in $y$ divided by the change in $x$ between two points on the line.

From the graph, let's identify two points on the line:

• Point 1: (0, -4) — where the line crosses the y-axis (this is also the y-intercept).
• Point 2: (4, 4).

The slope $m$ is calculated as: $m = \frac{\text{change in } y}{\text{change in } x} = \frac{4 - (-4)}{4 - 0} = \frac{8}{4} = 2$

Step 2: Identify the y-intercept $b$

From the graph, the line crosses the y-axis at $(0, -4)$, so the y-intercept $b = -4$.

Step 3: Write the equation

Now that we know the slope $m = 2$ and the y-intercept $b = -4$, we can write the equation in slope-intercept form: $y = 2x - 4$

This is the equation of the line.

Do you have any questions or need further clarification?

Here are 5 related questions for further practice:

1. What is the equation of a line with a slope of 3 and a y-intercept of 5?
2. How would the equation change if the line passed through $(0, 2)$ instead of $(0, -4)$?
3. If the slope were negative, say $-2$, how would the line's orientation change?
4. How do you determine the slope of a vertical line, and what is its equation?
5. Can two distinct lines with the same slope have different y-intercepts? Why?

Tip: Always check the coordinates of two points accurately to avoid errors in slope calculation!