The graph you provided shows a straight line with negative slope, crossing the x-axis at a point and the y-axis at another point. We can determine the equation of the line using the slope-intercept form $y = mx + b$, where:

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

Steps to determine the equation:

1. Identify the y-intercept (b): The line crosses the y-axis at $y = 4$, so the y-intercept $b = 4$.

2. Determine the slope (m): Slope $m$ is calculated as $\frac{\text{change in } y}{\text{change in } x}$. From the graph, one noticeable point is at $(-4, 0)$, and the y-intercept is $(0, 4)$. So: $m = \frac{4 - 0}{0 - (-4)} = \frac{4}{4} = 1$ The slope is negative due to the downward direction of the line, so $m = -1$.

Equation:

Now that we have $m = -1$ and $b = 4$, the equation of the line is: $y = -x + 4$

Would you like more details, or do you have any questions?

Here are 5 related questions you could explore:

1. How can we find the slope of a line using two points?
2. What does the y-intercept tell us about a graph?
3. How would the graph change if the slope were positive?
4. How can we rewrite this equation in standard form $Ax + By = C$?
5. What would the equation be if the line passed through the origin?

Tip: When graphing a line, always look for clear intercepts on the axes to easily determine the slope and equation.