Let's analyze the graph to find the equation of the straight line.

We need to express the equation in the form $y = mx + c$, where:

• $m$ is the slope of the line (rise over run).
• $c$ is the y-intercept (the point where the line crosses the y-axis).

Step 1: Identify two points on the line

From the graph, we can see that the line passes through the following points:

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

Step 2: Calculate the slope ($m$)

The slope is given by: $m = \frac{\text{change in } y}{\text{change in } x} = \frac{y_2 - y_1}{x_2 - x_1}$ Using the points $(-6, 0)$ and $(0, 6)$: $m = \frac{6 - 0}{0 - (-6)} = \frac{6}{6} = 1$ So, the slope $m = 1$.

Step 3: Identify the y-intercept ($c$)

From the graph, it's clear that the y-intercept $c$ is 6 (the point where the line crosses the y-axis).

Final Equation:

The equation of the line is: $y = 1x + 6 \quad \text{or simply} \quad y = x + 6$

Would you like more details or have any questions about this?

Further Related Questions:

1. How do you find the equation of a line if you only know the slope and one point?
2. What happens to the equation of a line when the slope is negative?
3. How can we determine the slope if the points are fractions or decimals?
4. What is the general form of a straight line equation?
5. How does the y-intercept affect the position of the line on the graph?

Tip: When calculating the slope, remember that it represents how steep a line is, with positive slopes going up and negative slopes going down.