Let's analyze the graph to find the slope and equation of the line.

1. Slope Calculation

The slope of a line is calculated using the formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$ From the graph, let’s identify two points on the line:

• Point 1: $(0, 2)$ (y-intercept)
• Point 2: $(4, -1)$

Substitute these values into the slope formula: $m = \frac{-1 - 2}{4 - 0} = \frac{-3}{4}$ Thus, the slope is: $\boxed{-\frac{3}{4}}$

2. Equation of the Line

The equation of a line in slope-intercept form is: $y = mx + b$

• From the slope calculation, $m = -\frac{3}{4}$.
• The $y$-intercept ($b$) is the point where the line crosses the $y$-axis. From the graph, $b = 2$.

Substitute $m$ and $b$ into the equation: $y = -\frac{3}{4}x + 2$

Thus, the equation of the line is: $\boxed{y = -\frac{3}{4}x + 2}$

Do you want further clarification on these calculations or have additional questions? Here are related topics for exploration:

1. How to calculate the slope using two points from the graph?
2. What is the significance of the $y$-intercept in a linear equation?
3. How can we rewrite this equation in standard form ($Ax + By = C$)?
4. How to interpret negative slopes in real-life scenarios?
5. What are parallel and perpendicular lines based on this slope?

Tip: The slope reveals how steep a line is; a negative slope indicates the line is decreasing as $x$ increases.