The graph shows a straight line, so the equation will be in the form of $y = mx + b$, where:

• $m$ is the slope (rate of change of the line).
• $b$ is the y-intercept (the value of $y$ when $x = 0$).

Step 1: Determine the slope ($m$)

To calculate the slope, we can use two points on the line. From the image:

• The line passes through the point $(0, -2)$ (the y-intercept).
• Another point the line passes through is approximately $(4, 2)$.

The formula for slope is: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Substitute $(x_1, y_1) = (0, -2)$ and $(x_2, y_2) = (4, 2)$: $m = \frac{2 - (-2)}{4 - 0} = \frac{4}{4} = 1$ So, the slope $m = 1$.

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

From the graph, the line crosses the y-axis at $y = -2$. Thus, the y-intercept $b = -2$.

Conclusion:

The equation of the line is: $y = x - 2$

Would you like further explanation or have any questions? Here are five related questions to expand on this:

1. How do you find the equation of a line if you are given two points?
2. What is the significance of the slope in a linear equation?
3. How do parallel lines relate in terms of slope?
4. How can we find the x-intercept of this line?
5. How do you graph a line given its equation?

Tip: To quickly determine the slope visually, count the vertical and horizontal distance between two points on the line (rise over run).