The red line in the graph appears to be a straight line, meaning it represents a linear equation. To find the equation of the line, we need two key pieces of information:

1. Slope (m): The slope is the ratio of the vertical change ("rise") to the horizontal change ("run").
2. Y-intercept (b): The y-intercept is the point where the line crosses the y-axis.

Step 1: Identify two points on the line

From the image, two points that the line clearly passes through are:

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

Step 2: Calculate the slope (m)

The slope $m$ is given by:

$m = \frac{{y_2 - y_1}}{{x_2 - x_1}} = \frac{{2 - (-4)}}{{4 - 2}} = \frac{{6}}{{2}} = 3$

So, the slope $m = 3$.

Step 3: Use the slope-intercept form

The slope-intercept form of a line is:

$y = mx + b$

We know $m = 3$, so we substitute one of the points into the equation to solve for $b$. Using the point $(2, -4)$:

$-4 = 3(2) + b$ $-4 = 6 + b$ $b = -4 - 6 = -10$

Final equation of the line:

$y = 3x - 10$

This is the equation of the red line in the graph.

Would you like further clarification or details on any step? Here are 5 related questions to explore further:

1. What is the significance of the slope and y-intercept in linear equations?
2. How would the graph change if the slope was negative?
3. What is the general process for converting between slope-intercept form and standard form?
4. Can you determine the x-intercept of the line from the equation?
5. How can you graph a line if you're given the equation directly?

Tip: When graphing lines, identifying clear points where the line crosses grid intersections can make finding the slope easier.