To find the equation of the line shown in the graph, we need to determine the slope and the y-intercept of the line. Let's start by identifying two points on the line from the graph.

From the image, the two points where the line passes through the grid are approximately:

• Point A: (-6, 0)
• Point B: (4, 4)

Step 1: Calculate the Slope (m)

The slope of the line ($m$) is calculated using the formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$

Using the coordinates of Point A $(-6, 0)$ and Point B $(4, 4)$: $m = \frac{4 - 0}{4 - (-6)} = \frac{4}{4 + 6} = \frac{4}{10} = \frac{2}{5}$

Step 2: Find the Y-intercept (b)

The y-intercept ($b$) is where the line crosses the y-axis. We can use the point-slope form of the equation to solve for $b$. The point-slope form is: $y = mx + b$

Using Point B $(4, 4)$: $4 = \frac{2}{5}(4) + b$ $4 = \frac{8}{5} + b$ $b = 4 - \frac{8}{5}$ $b = \frac{20}{5} - \frac{8}{5}$ $b = \frac{12}{5}$

Step 3: Write the Equation of the Line

Now that we have both the slope and the y-intercept, we can write the equation of the line in slope-intercept form: $y = \frac{2}{5}x + \frac{12}{5}$

Thus, the equation of the line is: $y = \frac{2}{5}x + \frac{12}{5}$

Would you like more details or have any questions?

Here are 5 related questions to expand your understanding:

1. How do you convert the equation $y = \frac{2}{5}x + \frac{12}{5}$ into standard form $Ax + By = C$?
2. What is the significance of the slope and y-intercept in the context of linear equations?
3. How can you find the equation of a line given only its graph without specific points?
4. What is the difference between the slope-intercept form and point-slope form of a linear equation?
5. How can you determine the x-intercept of the line from its equation?

Tip: To verify the accuracy of your equation, substitute the coordinates of the given points into your equation to see if they satisfy it.