This is a linear graph, and it appears to represent a linear function. To find the equation of the line, we will follow these steps:

Step 1: Identify two points on the line

From the image, two points that are easy to read from the graph are:

• $(0, 0)$ (the origin)
• $(5, 3)$ (from the graph, we can see that at $x = 5$, $y = 3$).

Step 2: Find the slope (m)

The slope of a line is calculated by the formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Using the points $(0, 0)$ and $(5, 3)$, we substitute: $m = \frac{3 - 0}{5 - 0} = \frac{3}{5}$ So, the slope of the line is $\frac{3}{5}$.

Step 3: Use the point-slope form to find the equation of the line

The point-slope form of a line equation is given by: $y - y_1 = m(x - x_1)$ Using the point $(0, 0)$ and the slope $\frac{3}{5}$, we substitute into the equation: $y - 0 = \frac{3}{5}(x - 0)$ This simplifies to: $y = \frac{3}{5}x$

Step 4: Conclusion

The equation of the line is: $y = \frac{3}{5}x$

This is the linear equation represented by the graph.

Would you like more details on any step, or do you have further questions?

Here are five questions to expand on this:

1. How do you interpret the slope in the context of this graph?
2. What is the significance of the y-intercept in this line?
3. How would the equation change if the line passed through a different point?
4. What is the general form of a linear equation, and how does this example fit?
5. Can you find the x-value when $y = 6$ using the equation of the line?

Tip:

For linear graphs, always start by identifying two distinct points to calculate the slope, as it gives you a direct path to form the equation.