To write the equation of this line in slope-intercept form, we need two key pieces of information:

1. The slope (m): The slope is the "rise over run" between two points on the line.
2. The y-intercept (b): This is where the line crosses the y-axis.

Step 1: Identify the y-intercept (b)

From the graph, it appears that the line crosses the y-axis at $y = 1$. Therefore, $b = 1$.

Step 2: Calculate the slope (m)

To calculate the slope, we need two points on the line. I will choose:

• Point 1: $(0, 1)$, the y-intercept.
• Point 2: $(2, 0)$, where the line crosses the x-axis.

Now, use the slope formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Substituting the points: $m = \frac{0 - 1}{2 - 0} = \frac{-1}{2}$

So, the slope is $m = -\frac{1}{2}$.

Step 3: Write the equation

The slope-intercept form is: $y = mx + b$ Substitute the slope $m = -\frac{1}{2}$ and the y-intercept $b = 1$: $y = -\frac{1}{2}x + 1$

Thus, the equation of the line is: $y = -\frac{1}{2}x + 1$

Would you like any further explanation on this?

Here are 5 follow-up questions:

1. How do we calculate the slope of a line given two points?
2. What is the meaning of the y-intercept in a linear equation?
3. How would the equation change if the slope were positive?
4. Can you find another point on the line and verify the slope?
5. How can we rearrange this equation to standard form?

Tip: The slope can tell you the direction of the line; if it's negative, the line slopes downwards!