The image shows a line graphed on a coordinate plane. To analyze the line, I will first extract the important points and properties from the graph.

Step 1: Identify the coordinates

Based on the image, the line passes through two points:

• The first point is approximately at (-2, 1).
• The second point is at (2, 3).

Step 2: Calculate the slope

The formula for the slope $m$ between two points $(x_1, y_1)$ and $(x_2, y_2)$ is: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Substituting the points (-2, 1) and (2, 3): $m = \frac{3 - 1}{2 - (-2)} = \frac{2}{4} = \frac{1}{2}$

Step 3: Find the equation of the line

Using the slope-intercept form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept, we can find $b$.

Substituting $m = \frac{1}{2}$ and one of the points, say (2, 3): $3 = \frac{1}{2}(2) + b \implies 3 = 1 + b \implies b = 2$

Thus, the equation of the line is: $y = \frac{1}{2}x + 2$

Would you like me to explain anything in more detail or perform additional analyses?

5 Related Questions:

1. How can you determine if a line is increasing or decreasing based on its slope?
2. What are the different forms of linear equations, and how can you convert between them?
3. How do you find the distance between two points on a graph?
4. What does the y-intercept represent in a linear equation?
5. How can you determine the x-intercept from the equation of a line?

Tip: The slope of a line tells you how steep the line is and the direction it travels. Positive slopes rise to the right, while negative slopes fall to the right.