To write the equation of the line in slope-intercept form, which is $y = mx + b$, we need the slope ($m$) and the y-intercept ($b$) of the line.

Step 1: Identify the Slope ($m$)

The slope is the "rise over run," or the change in $y$ divided by the change in $x$ between two points on the line. From the graph:

• Choose two clear points where the line crosses grid intersections. For example, we can see the line passes through $(0, 3)$ and $(3, 0)$.
• Calculate the slope: $m = \frac{\text{change in } y}{\text{change in } x} = \frac{0 - 3}{3 - 0} = \frac{-3}{3} = -1$

Step 2: Identify the y-intercept ($b$)

The y-intercept is the point where the line crosses the y-axis. From the graph, we see that the line crosses the y-axis at $(0, 3)$, so $b = 3$.

Step 3: Write the Equation

Now that we have $m = -1$ and $b = 3$, the equation of the line in slope-intercept form is: $y = -x + 3$

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

1. How do you determine the slope from two points on a line?
2. What is the significance of the y-intercept in a linear equation?
3. How can you identify if a slope is positive or negative by looking at the line?
4. How would the equation change if the line crossed the y-axis at a different point?
5. What does it mean if the slope of a line is zero?

Tip: When writing equations from a graph, use clear intersection points to minimize calculation errors.