To write an equation in slope-intercept form for the line in the graph, we can follow these steps:

1. Identify the Slope (m):

The slope-intercept form of a line is $y = mx + b$, where:

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

Looking at the graph:

• The line appears to go downwards from left to right, indicating a negative slope.
• Choose two clear points on the line to calculate the slope. Based on the grid:
  • One point is at (0, 3), the y-intercept.
  • Another point is at (3, 0).

Using these two points: $\text{slope } m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - 3}{3 - 0} = \frac{-3}{3} = -1$

So, the slope $m$ is -1.

2. Identify the Y-intercept (b):

From the graph, we can see that the line crosses the y-axis at (0, 3). Therefore, the y-intercept $b$ is 3.

3. Write the Equation:

Now that we know the slope $m = -1$ and the y-intercept $b = 3$, we can write the equation: $y = -x + 3$

Final Answer:

The equation of the line in slope-intercept form is: $y = -x + 3$

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

Here are 5 related questions:

1. How do you determine the slope if the line passes through two different points?
2. How would the equation change if the line had a positive slope?
3. What happens to the equation if the line passes through the origin?
4. How do you convert slope-intercept form to standard form?
5. What does it mean if the slope of a line is zero?

Tip: When identifying the slope from a graph, look for two points where the line intersects the grid clearly for accurate slope calculation.