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

Step 1: Identify the y-intercept

The y-intercept is the point where the line crosses the y-axis. From the graph, the line crosses the y-axis at $(0, 3)$. So, the y-intercept $b = 3$.

Step 2: Determine the slope

The slope $m$ can be calculated using two points on the line. From the graph, let's use the points $(0, 3)$ and $(3, 0)$.

Using the slope formula: $m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - 3}{3 - 0} = \frac{-3}{3} = -1$

Step 3: Write the equation of the line

Using the slope-intercept form $y = mx + b$, we substitute the values of $m$ and $b$:

$y = -x + 3$

So, the equation of the line is:

$y = -x + 3$

Would you like more details or have any other questions?

Related Questions:

1. How do you find the equation of a line given two points?
2. What is the significance of the slope and y-intercept in a linear equation?
3. How do you determine the slope from a graph?
4. What changes occur to the line's equation if the slope or y-intercept is altered?
5. How can you convert a linear equation from standard form to slope-intercept form?

Tip: When finding the slope of a line from a graph, use clear points where the line crosses grid lines to ensure accuracy.