The equation given in the image is:

$y = -\frac{2}{5}x - 5$

This is the equation of a line in slope-intercept form, where $y = mx + b$, with:

• $m = -\frac{2}{5}$ (the slope)
• $b = -5$ (the y-intercept)

Steps to analyze the graph:

1. Y-Intercept: The y-intercept is at $y = -5$, which is where the line crosses the y-axis. On the graph, you can observe the line crossing the y-axis at the point (0, -5).
2. Slope: The slope of $-\frac{2}{5}$ means that for every 5 units you move to the right (positive x direction), the line goes down by 2 units (negative y direction). This explains the downward trend of the line.

Verifying points:

From the graph, it looks like two specific points have been highlighted:

• $(-5, -3)$ is one of the points on the left side.
• $(5, -7)$ is another point on the right side.

Checking if these points satisfy the equation:

For $(-5, -3)$: $y = -\frac{2}{5}(-5) - 5 = 2 - 5 = -3$ This point satisfies the equation.

For $(5, -7)$: $y = -\frac{2}{5}(5) - 5 = -2 - 5 = -7$ This point also satisfies the equation.

Therefore, the points plotted are correct representations of the line $y = -\frac{2}{5}x - 5$.

Would you like more details on any part of this explanation or further analysis?

Here are five related questions:

1. How do you calculate the slope from two points?
2. How would you rewrite this equation in standard form?
3. What would the graph look like if the slope were positive?
4. How can you find the x-intercept of this line?
5. What happens to the graph if you change the y-intercept?

Tip: The slope of a line determines its direction. A negative slope means the line goes down as you move from left to right.