The equation of a straight line is typically written as:

$y = mx + b$

Where:

• $m$ is the slope of the line.
• $b$ is the y-intercept, the value where the line crosses the y-axis.

Step 1: Find the slope ($m$)

The slope $m$ is calculated as:

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

From the graph, two clear points on the line are:

• Point 1: $(-6, -8)$
• Point 2: $(0, -2)$

Now calculate the slope:

$m = \frac{{-2 - (-8)}}{{0 - (-6)}} = \frac{{-2 + 8}}{{6}} = \frac{6}{6} = 1$

Thus, the slope $m = 1$.

Step 2: Find the y-intercept ($b$)

The y-intercept is the point where the line crosses the y-axis. From the graph, the line crosses the y-axis at the point $(0, -2)$.

Thus, $b = -2$.

Conclusion:

$m = 1 \quad \text{and} \quad b = -2$

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

Here are five related questions:

1. How can the slope be negative, and what would it mean for the graph?
2. What would change if the y-intercept was positive?
3. How does changing the slope affect the steepness of the line?
4. What is the general formula for finding the slope between two points?
5. Can a line have a slope of zero, and how would that look on a graph?

Tip: To quickly find the slope of a line, remember that slope represents the "rise over run," or how much the line goes up or down compared to how much it moves horizontally!