To write the equation of the line shown in the graph, we need to determine its slope and y-intercept.

Step 1: Determine the slope ($m$)

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

From the graph, the line passes through the points:

• $(0, 3)$
• $(4, 5)$

Using these points: $m = \frac{5 - 3}{4 - 0} = \frac{2}{4} = \frac{1}{2}$

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

The y-intercept is where the line crosses the $y$-axis. From the graph, the y-intercept is clearly $b = 3$.

Step 3: Write the equation of the line

Using the slope-intercept form of a line ($y = mx + b$), the equation is: $y = \frac{1}{2}x + 3$

This is the equation of the line. Let me know if you'd like further details!

Here are 5 related questions for practice:

1. How would the equation change if the slope were $2$ instead of $\frac{1}{2}$?
2. How do you determine the slope if given two different points?
3. What happens to the graph if the y-intercept changes to $b = -2$?
4. How do you convert this equation to standard form ($Ax + By = C$)?
5. Can you write an equation for a line parallel to this one?

Tip: Always identify the slope and y-intercept clearly from the graph or points provided before writing the equation.