To solve the problem of finding the slope using rise over run for each graph, we need to follow these steps:
1.
Identify the Rise (\(\Delta y\)): This is the vertical change in the graph (upward or downward).
2.
Identify the Run (\(\Delta x\)): This is the horizontal change in the graph (rightward or leftward).
3.
Calculate the Slope: The slope is given by the formula:
\[
\text{Slope} = \frac{\Delta y}{\Delta x}
\]
Let's go through each graph step by step.
---
Graph (1)
-
Rise (\(\Delta y\)): The line moves downward by 4 units.
-
Run (\(\Delta x\)): The line moves rightward by 6 units.
-
Slope:
\[
\text{Slope} = \frac{\Delta y}{\Delta x} = \frac{-4}{6} = -\frac{2}{3}
\]
---
Graph (2)
-
Rise (\(\Delta y\)): The line moves downward by 3 units.
-
Run (\(\Delta x\)): The line moves rightward by 2 units.
-
Slope:
\[
\text{Slope} = \frac{\Delta y}{\Delta x} = \frac{-3}{2}
\]
---
Graph (3)
-
Rise (\(\Delta y\)): The line moves upward by 4 units.
-
Run (\(\Delta x\)): The line moves rightward by 4 units.
-
Slope:
\[
\text{Slope} = \frac{\Delta y}{\Delta x} = \frac{4}{4} = 1
\]
---
Graph (4)
-
Rise (\(\Delta y\)): The line moves upward by 3 units.
-
Run (\(\Delta x\)): The line moves rightward by 6 units.
-
Slope:
\[
\text{Slope} = \frac{\Delta y}{\Delta x} = \frac{3}{6} = \frac{1}{2}
\]
---
Graph (5)
-
Rise (\(\Delta y\)): The line moves upward by 6 units.
-
Run (\(\Delta x\)): The line does not move horizontally (run = 0).
-
Slope:
\[
\text{Slope} = \frac{\Delta y}{\Delta x} = \frac{6}{0} = \text{undefined}
\]
(Vertical lines have undefined slopes.)
---
Graph (6)
-
Rise (\(\Delta y\)): The line does not move vertically (rise = 0).
-
Run (\(\Delta x\)): The line moves rightward by 6 units.
-
Slope:
\[
\text{Slope} = \frac{\Delta y}{\Delta x} = \frac{0}{6} = 0
\]
(Horizontal lines have a slope of 0.)
---
Graph (7)
-
Rise (\(\Delta y\)): The line moves downward by 6 units.
-
Run (\(\Delta x\)): The line moves rightward by 4 units.
-
Slope:
\[
\text{Slope} = \frac{\Delta y}{\Delta x} = \frac{-6}{4} = -\frac{3}{2}
\]
---
Graph (8)
-
Rise (\(\Delta y\)): The line moves upward by 2 units.
-
Run (\(\Delta x\)): The line moves rightward by 4 units.
-
Slope:
\[
\text{Slope} = \frac{\Delta y}{\Delta x} = \frac{2}{4} = \frac{1}{2}
\]
---
Graph (9)
-
Rise (\(\Delta y\)): The line moves upward by 4 units.
-
Run (\(\Delta x\)): The line moves rightward by 2 units.
-
Slope:
\[
\text{Slope} = \frac{\Delta y}{\Delta x} = \frac{4}{2} = 2
\]
---
Final Answers
\[
\boxed{
\begin{array}{ccc}
\text{Graph (1)} & \text{Slope} = -\frac{2}{3} \\
\text{Graph (2)} & \text{Slope} = -\frac{3}{2} \\
\text{Graph (3)} & \text{Slope} = 1 \\
\text{Graph (4)} & \text{Slope} = \frac{1}{2} \\
\text{Graph (5)} & \text{Slope} = \text{undefined} \\
\text{Graph (6)} & \text{Slope} = 0 \\
\text{Graph (7)} & \text{Slope} = -\frac{3}{2} \\
\text{Graph (8)} & \text{Slope} = \frac{1}{2} \\
\text{Graph (9)} & \text{Slope} = 2 \\
\end{array}
}
\]
Parent Tip: Review the logic above to help your child master the concept of rise over run worksheet.
