From the graph, we need to find the equation of the straight line in the form $y = mx + c$, where $m$ is the slope and $c$ is the y-intercept.

Step 1: Find the slope ($m$)

The slope is calculated using two points on the line: $m = \frac{\Delta y}{\Delta x}$

From the graph:

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

Using these points: $m = \frac{8 - 0}{0 - (-6)} = \frac{8}{6} = \frac{4}{3}$

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

The y-intercept is the value of $y$ when $x = 0$. From the graph, the line crosses the y-axis at $c = 8$.

Final Equation

Substitute $m = \frac{4}{3}$ and $c = 8$ into the equation: $y = \frac{4}{3}x + 8$

Let me know if you need further details or explanations!

Related Questions:

1. How is the slope of a line calculated between two points?
2. Why is the y-intercept value important in the equation of a line?
3. How would the equation change if the line were steeper?
4. Can you rewrite this equation in standard form ($Ax + By + C = 0$)?
5. What happens to the line if the slope is negative?

Tip: Always use clear, simple points on the graph to calculate the slope for accuracy.