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

1. Identify two points on the line to calculate the slope ($m$).
2. Determine the y-intercept $b$, which is where the line crosses the y-axis.

From the image:

• The line appears to pass through two points: $(0, 0)$ and $(2, 4)$.

Step 1: Calculate the slope $m$

The formula for the slope is: $m = \frac{y_2 - y_1}{x_2 - x_1}$

Using the points $(0, 0)$ and $(2, 4)$: $m = \frac{4 - 0}{2 - 0} = \frac{4}{2} = 2$ So, the slope $m = 2$.

Step 2: Identify the y-intercept $b$

Since the line passes through the origin $(0, 0)$, the y-intercept $b = 0$.

Final equation of the line:

$y = 2x$

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

Would you like more details or have any further questions?

Relative questions:

1. What is the general process to calculate the slope of a line?
2. How do you find the y-intercept if the line doesn't pass through the origin?
3. How can you derive the equation of a line if given two points?
4. How does the slope affect the angle of the line?
5. What is the equation for a vertical line, and why is its slope undefined?

Tip: Always check the coordinates of points used to calculate the slope accurately, as this step is crucial for finding the correct equation.