We can derive the equation of the line from the graph in slope-intercept form, which is:

$y = mx + b$

Where:

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

Step 1: Find the slope (m)

The slope is the change in y divided by the change in x, or:

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

From the graph, we can use the two points:

• $(0, -2)$
• $(1, 3)$

Plugging these into the slope formula:

$m = \frac{3 - (-2)}{1 - 0} = \frac{5}{1} = 5$

So, the slope $m = 5$.

Step 2: Determine the y-intercept (b)

From the graph, we can see that the line crosses the y-axis at the point $(0, -2)$. Therefore, the y-intercept $b = -2$.

Step 3: Write the equation

Now, we can substitute the slope $m = 5$ and the y-intercept $b = -2$ into the slope-intercept form:

$y = 5x - 2$

Thus, the equation of the line is:

$y = 5x - 2$

Would you like more details, or have any other questions? Here are some related questions you might consider:

1. What does the slope of a line represent in real-world scenarios?
2. How can we find the equation of a line given any two points?
3. How does changing the slope or intercept affect the graph of a line?
4. What is the point-slope form of the equation of a line, and how is it derived?
5. How can the slope-intercept form be used to solve real-life problems?

Tip: The slope of a line determines its steepness. A larger slope means the line is steeper, while a negative slope means the line slopes downward.