To find the equation of the line shown on the graph, we need two pieces of information:

1. Slope (m): The slope is the "rise over run," or how much the line goes up (change in $y$) for every unit it goes to the right (change in $x$).
2. y-intercept (b): The value where the line crosses the $y$-axis.

Step 1: Identify two points on the line

From the graph, two points the line passes through are:

• Point 1: $(0, 1)$ (the line crosses the $y$-axis at $y = 1$)
• Point 2: $(10, 5)$ (the line also passes through $x = 10$, $y = 5$)

Step 2: Calculate the slope (m)

The formula for the slope is: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Using the points $(0, 1)$ and $(10, 5)$: $m = \frac{5 - 1}{10 - 0} = \frac{4}{10} = 0.4$

Step 3: Write the equation of the line

The slope-intercept form of the equation of a line is: $y = mx + b$ From the graph, the line crosses the $y$-axis at $y = 1$, so $b = 1$.

Thus, the equation of the line is: $y = 0.4x + 1$

Would you like any further explanation, or have any specific questions?

Follow-up questions:

1. What is the general form of a linear equation?
2. How is the slope of a line interpreted geometrically?
3. Can you calculate the slope if the points are closer, such as $(0, 1)$ and $(5, 3)$?
4. How does the value of the slope affect the steepness of the line?
5. What happens to the equation of the line if it passes through the origin?

Tip:

When identifying points to calculate the slope, try to choose points that are clearly on the grid to avoid errors in estimation.