The image shows a straight line on a coordinate plane. To write the equation of this line, we need two key pieces of information:

1. Slope (m): The slope is the "rise over run," or the change in the y-values divided by the change in the x-values.
2. y-intercept (b): This is the point where the line crosses the y-axis.

Step 1: Identify two points on the line

We can read the coordinates of two points on the graph:

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

Step 2: Calculate the slope (m)

The formula for the slope is: $m = \frac{{y_2 - y_1}}{{x_2 - x_1}}$ Using the points (0, -2) and (2, 2): $m = \frac{{2 - (-2)}}{{2 - 0}} = \frac{4}{2} = 2$

Step 3: Write the equation in slope-intercept form

The general form of a line is: $y = mx + b$ We already know that $m = 2$ and the y-intercept (b) is -2, since the line crosses the y-axis at (0, -2). So the equation of the line is: $y = 2x - 2$

Thus, the equation of the line is $y = 2x - 2$.

Would you like more details or have any questions?

Here are some related questions to consider:

1. What is the significance of the slope in a line's equation?
2. How would the equation change if the line had a negative slope?
3. What is the difference between slope-intercept form and standard form of a linear equation?
4. How do you find the x-intercept from the equation of a line?
5. What happens to the graph if we change the y-intercept?

Tip: The slope defines how steep the line is, and it affects the direction (upward or downward) of the line.