To find the equation of the line shown in the graph, follow these steps:

Step 1: Identify the slope ($m$)

The slope is defined as the change in $y$ over the change in $x$:
$m = \frac{y_2 - y_1}{x_2 - x_1}$

From the graph:

• Two clear points on the line are $(0, 2)$ (the y-intercept) and $(2, 0)$.

Now, calculate the slope: $m = \frac{0 - 2}{2 - 0} = \frac{-2}{2} = -1$

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

From the graph, the line crosses the y-axis at $y = 2$. Hence, the y-intercept is: $b = 2$

Step 3: Write the equation of the line

Using the slope-intercept form $y = mx + b$, we have: $y = -x + 2$

Final Answer

$\boxed{y = -x + 2}$

Do you have any questions or would you like more explanation?
Here are 5 related questions you can explore for practice:

1. What is the slope of a line perpendicular to this one?
2. How do you find the x-intercept of a line?
3. If the y-intercept was changed to -3, how would the equation change?
4. How can you rewrite the equation in standard form $Ax + By = C$?
5. What are the conditions for two lines to be parallel?

Tip: The slope of a line determines its steepness and direction—positive slopes go up, while negative slopes go down from left to right.