To solve the problem, we will analyze the given graph and determine the slope-intercept form of the line. The slope-intercept form of a line is:

$y = mx + b$

Where:

• $m$ is the slope of the line.
• $b$ is the y-intercept (the point where the line crosses the $y$-axis).

Step 1: Determine the slope $m$

The slope $m$ is calculated as: $m = \frac{\text{rise}}{\text{run}}$

Looking at the graph:

• The line passes through two points, approximately $(0, 2)$ (the $y$-intercept) and $(-2, 0)$.
• The "rise" is the vertical change: $2 - 0 = 2$.
• The "run" is the horizontal change: $0 - (-2) = 2$.

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

Step 2: Determine the y-intercept $b$

The y-intercept $b$ is where the line crosses the $y$-axis. From the graph, the line crosses the $y$-axis at $y = 2$, so $b = 2$.

Step 3: Write the equation

Substitute $m = -1$ and $b = 2$ into the slope-intercept form: $y = -x + 2$

Final Answer:

The equation of the line in slope-intercept form is: $y = -x + 2$

Would you like more explanation, or do you have any additional questions?

Follow-up Questions:

1. How is the slope calculated when the graph is not easily readable?
2. What does a positive slope look like compared to a negative slope?
3. How do you calculate the slope when given two points on the line?
4. Can you rewrite this equation in standard form ($Ax + By = C$)?
5. What happens to the graph if the slope or $y$-intercept is changed?

Tip:

When finding the slope visually, always move from one point to another along the grid to count the "rise" and "run" accurately!