To solve the problem and determine the slopes of the lines, we will apply the slope formula:

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

This formula calculates the rate of change between two points on the line. The slope represents how much $y$ changes for each unit change in $x$.

Let's analyze each graph to determine the slopes.

Graph 1:

1. The line is increasing, and by inspecting the grid, we can see it rises 1 unit up for every 1 unit to the right. This gives a slope of: $\text{slope} = \frac{1}{1} = 1$

Graph 2:

2. The line is also increasing, and the rise is 2 units up for every 1 unit to the right. This gives a slope of: $\text{slope} = \frac{2}{1} = 2$

Graph 3:

3. The line is decreasing, and it falls 1 unit down for every 2 units to the right. This gives a negative slope of: $\text{slope} = \frac{-1}{2} = -\frac{1}{2}$

Final Results:

• Graph 1: Slope = 1
• Graph 2: Slope = 2
• Graph 3: Slope = -1/2

Would you like further details or clarifications?

Related Questions:

1. How can you calculate the slope if given two points on a line?
2. What does a slope of zero represent in terms of a line's appearance?
3. How can negative slopes be interpreted in real-world contexts?
4. How does the slope affect the angle of inclination of a line?
5. What is the significance of the slope in linear equations?

Tip: A positive slope indicates a line that rises as you move to the right, while a negative slope indicates a line that falls.