Let's analyze the graph in the image to determine the equation of the line in slope-intercept form, which is generally written as:

$y = mx + b$

Where:

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

Step 1: Find the slope ($m$)

To calculate the slope, use the formula:

$m = \frac{{y_2 - y_1}}{{x_2 - x_1}}$

From the graph, we can see that two points on the line are:

• Point 1: $(0, 4)$, where the line crosses the y-axis.
• Point 2: $(4, 0)$, where the line crosses the x-axis.

Now, plug the coordinates into the slope formula:

$m = \frac{{0 - 4}}{{4 - 0}} = \frac{{-4}}{{4}} = -1$

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

The y-intercept is the value of $y$ when $x = 0$. From the graph, we can clearly see that the line crosses the y-axis at $y = 4$, so:

$b = 4$

Step 3: Write the equation

Now that we have the slope ($m = -1$) and the y-intercept ($b = 4$), we can write the equation of the line:

$y = -x + 4$

This is the equation of the line in slope-intercept form.

Would you like more details or have any questions?

Related Questions:

1. How do you determine the slope from a graph?
2. What is the significance of the y-intercept in an equation?
3. How does a negative slope affect the direction of the line?
4. How can you verify the equation by using another point on the line?
5. What happens if a line is vertical or horizontal—how do their equations differ?

Tip: When finding the slope, always pick two clearly defined points to avoid calculation errors.