Looking at the graph you uploaded, it appears that the red line represents a linear equation, and we need to determine its slope-intercept form, which is typically written as:

$y = mx + b$

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 $m$

To calculate the slope, we need two points on the line. From the image, the line appears to pass through:

• Point $(0, 2)$ on the y-axis.
• Point $(-2, 4)$.

The slope formula is:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Using the points $(0, 2)$ and $(-2, 4)$:

$m = \frac{4 - 2}{-2 - 0} = \frac{2}{-2} = -1$

So, the slope $m = -1$.

Step 2: Determine the y-intercept $b$

From the graph, we can see that the line crosses the y-axis at $y = 2$, so the y-intercept $b = 2$.

Final Equation

Thus, the equation of the line is:

$y = -x + 2$

Would you like a more detailed explanation or have any questions?

Here are 5 related questions to expand on this topic:

1. What does the slope of a line tell us about its direction?
2. How can we calculate the slope if we only have the graph and no points given?
3. What happens to the line if the y-intercept changes?
4. How does the slope affect the steepness of a line?
5. Can a line have an undefined slope, and how would it look on a graph?

Tip: To quickly identify the slope from a graph, count the vertical change ("rise") and the horizontal change ("run") between any two points on the line.