From the image provided, the graph shows a line with points labeled $(3, 4)$ and $(5, 5)$. Let's determine the equation of the line in point-slope form.

Step 1: Find the slope $m$

The formula for the slope $m$ is: $m = \frac{y_2 - y_1}{x_2 - x_1}$

Substitute $(x_1, y_1) = (3, 4)$ and $(x_2, y_2) = (5, 5)$: $m = \frac{5 - 4}{5 - 3} = \frac{1}{2}$

So, the slope is $m = \frac{1}{2}$.

Step 2: Use the point-slope form

The point-slope form of a line is: $y - y_1 = m(x - x_1)$

Using the point $(3, 4)$ and $m = \frac{1}{2}$: $y - 4 = \frac{1}{2}(x - 3)$

This is the equation of the line in point-slope form.

Final Answer:

The equation is: $y - 4 = \frac{1}{2}(x - 3)$

Would you like more details or additional examples?

Related Questions:

1. How do you convert a point-slope form equation to slope-intercept form?
2. What are other ways to write the equation of a line, such as in standard form?
3. How do you determine the slope if only a graph is given, without labeled points?
4. Why is point-slope form helpful compared to slope-intercept form?
5. What is the significance of the slope in real-world applications?

Tip:

Always double-check the points on the graph and ensure you subtract $y_2 - y_1$ and $x_2 - x_1$ in the correct order to avoid sign errors.