To determine the slope $m$ and y-intercept $b$ of the line shown in the graph, we can follow these steps:

1. Finding the slope $m$:

The slope of a line is calculated using the formula:

$m = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1}$

From the graph, let's choose two clear points on the line:

• Point 1: $(0, 3)$ (y-intercept)
• Point 2: $(6, 0)$

Now, applying the slope formula:

$m = \frac{0 - 3}{6 - 0} = \frac{-3}{6} = -\frac{1}{2}$

2. Finding the y-intercept $b$:

The y-intercept is the point where the line crosses the y-axis. From the graph, it's clear that the line crosses the y-axis at $(0, 3)$, so the y-intercept $b = 3$.

Conclusion:

• The slope $m = -\frac{1}{2}$
• The y-intercept $b = 3$

Do you want more details or have any questions?

Here are 5 related questions to explore:

1. How do you calculate the slope if the points are not as clear?
2. Can you always calculate the slope using any two points on a line?
3. What does a positive slope versus a negative slope represent graphically?
4. How can the slope-intercept form $y = mx + b$ help in sketching a graph?
5. How does changing the y-intercept affect the position of the line?

Tip: Always verify that the points used for slope calculation lie exactly on the line to avoid rounding errors.