From the image, you have two points given: (2, 1) and (5, 3). There is also a table with two columns labeled $x$ and $y$, but it appears blank. This setup is likely for calculating or organizing the relationship between $x$ and $y$, possibly for finding the equation of the line that passes through these points.

Let's proceed by finding the equation of the line using the slope-intercept form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

Step 1: Calculate the slope $m$

The slope formula is: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Using the points $(2, 1)$ and $(5, 3)$: $m = \frac{3 - 1}{5 - 2} = \frac{2}{3}$

Step 2: Use the slope to find the equation

Now that we have the slope $m = \frac{2}{3}$, we substitute one of the points into the slope-intercept form to find $b$.

Using the point $(2, 1)$: $y = mx + b \quad \text{becomes} \quad 1 = \frac{2}{3}(2) + b$ $1 = \frac{4}{3} + b$ Subtract $\frac{4}{3}$ from both sides: $b = 1 - \frac{4}{3} = \frac{3}{3} - \frac{4}{3} = -\frac{1}{3}$

Final Equation

The equation of the line is: $y = \frac{2}{3}x - \frac{1}{3}$

Would you like to discuss this equation further, or should I help you complete the table with additional values for $x$ and $y$?

Here are some related questions:

1. How do you calculate the slope if given two points?
2. What is the slope-intercept form of a linear equation?
3. How do you find the y-intercept once the slope is known?
4. What is the significance of the y-intercept in a line equation?
5. How can you use the equation to predict other points on the line?

Tip: When you have two points, always start by calculating the slope to understand the relationship between $x$ and $y$.