Let's analyze the given graph and determine the equation of the straight line.

Step 1: Identify two points on the line

From the graph, two points the line passes through are:

• $(-6, 0)$ (x-intercept)
• $(0, 6)$ (y-intercept)

Step 2: Find the slope $m$

The formula for the slope between two points $(x_1, y_1)$ and $(x_2, y_2)$ is:

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

Substituting the points $(-6, 0)$ and $(0, 6)$:

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

Thus, the slope $m = 1$.

Step 3: Determine the y-intercept $c$

From the graph, the line crosses the y-axis at $y = 6$, so the y-intercept $c = 6$.

Step 4: Write the equation

Using the slope-intercept form:

$y = mx + c$

$y = 1x + 6$

Thus, the equation of the line is:

$\mathbf{y = x + 6}$

Would you like a detailed explanation of any step?

Here are some related questions you might find interesting:

1. How do you find the equation of a line given two points?
2. What is the significance of the slope in a linear equation?
3. How do you convert from slope-intercept form to standard form?
4. How can you determine if two lines are parallel or perpendicular?
5. What is the role of the y-intercept in real-life applications?

Tip: When identifying points on a graph, always look for clear grid intersections to ensure accuracy.