To write the equation of the graphed line, we can follow these steps:

Step 1: Identify the slope of the line

To find the slope, we can use two points on the line. From the graph, two clear points on the line are:

• (-5, 4)
• (5, 0)

The formula for the slope ($m$) is: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Substituting the points (-5, 4) and (5, 0): $m = \frac{0 - 4}{5 - (-5)} = \frac{-4}{10} = -\frac{2}{5}$ So, the slope is $-\frac{2}{5}$.

Step 2: Use the slope-intercept form

The equation of a line in slope-intercept form is: $y = mx + b$ where $m$ is the slope and $b$ is the y-intercept.

Step 3: Find the y-intercept ($b$)

From the graph, the line crosses the y-axis at $(0, 2)$. This means the y-intercept $b = 2$.

Step 4: Write the final equation

Now that we know the slope ($m = -\frac{2}{5}$) and the y-intercept ($b = 2$), the equation of the line is: $y = -\frac{2}{5}x + 2$

Would you like further details or have any questions?

Here are some related questions to practice:

1. How would the equation change if the slope were positive but with the same y-intercept?
2. What is the equation of a line parallel to this one that passes through the point (1, 3)?
3. Can you find the equation of the line that is perpendicular to this one and passes through the origin?
4. What happens to the equation if we shift the line upward by 3 units?
5. How can we express this equation in standard form (Ax + By = C)?

Tip:

To quickly determine the slope of a line from a graph, remember to choose points where the line clearly crosses grid intersections to avoid miscalculating.