finding slope using rise over run
name:
date:
to find the slope, divide the
ise\ (the change in y) by the
un\ (the change in x).
(1)
rise: $\delta y =$
run: $\delta x =$
slope:
(2)
rise: $\delta y =$
run: $\delta x =$
slope:
(3)
rise: $\delta y =$
run: $\delta x =$
slope:
(4)
rise: $\delta y =$
run: $\delta x =$
slope:
(5)
rise: $\delta y =$
run: $\delta x =$
slope:
(6)
rise: $\delta y =$
run: $\delta x =$
slope:
(7)
rise: $\delta y =$
run: $\delta x =$
slope:
(8)
rise: $\delta y =$
run: $\delta x =$
slope:
(9)
rise: $\delta y =$
run: $\delta x =$
slope:
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Question

finding slope using rise over run
name:
date:
to find the slope, divide the
ise\ (the change in y) by the
un\ (the change in x).
(1)
rise: $\delta y =$
run: $\delta x =$
slope:
(2)
rise: $\delta y =$
run: $\delta x =$
slope:
(3)
rise: $\delta y =$
run: $\delta x =$
slope:
(4)
rise: $\delta y =$
run: $\delta x =$
slope:
(5)
rise: $\delta y =$
run: $\delta x =$
slope:
(6)
rise: $\delta y =$
run: $\delta x =$
slope:
(7)
rise: $\delta y =$
run: $\delta x =$
slope:
(8)
rise: $\delta y =$
run: $\delta x =$
slope:
(9)
rise: $\delta y =$
run: $\delta x =$
slope:
copyright  worksheetworks.com

Accepted Answer

Let's solve problem (1) as an example:

# Explanation:
## Step1: Determine the change in y (Rise)
Looking at the line in the first graph, we can see that for a certain horizontal movement (run), the vertical movement (rise) is positive. Let's pick two points on the line. If we move from one point to another, say, the vertical change (Δy) is 3 (assuming each grid square is 1 unit, and we count the number of units we move up).
## Step2: Determine the change in x (Run)
The horizontal change (Δx) is 4 (counting the number of units we move to the right).
## Step3: Calculate the slope
The slope is calculated as $\frac{\Delta y}{\Delta x}$, so substituting the values we found, the slope is $\frac{3}{4}$.

# Answer:
For problem (1):
Rise ($\Delta y$) = 3
Run ($\Delta x$) = 4
Slope = $\frac{3}{4}$

We can follow a similar process for the other problems:

### Problem (2)
## Step1: Determine Δy
The line is steeper. The vertical change (rise) is 4 (moving up 4 units).
## Step2: Determine Δx
The horizontal change (run) is 2 (moving right 2 units).
## Step3: Calculate slope
Slope = $\frac{4}{2}$ = 2

# Answer:
Rise ($\Delta y$) = 4
Run ($\Delta x$) = 2
Slope = 2

### Problem (3)
## Step1: Determine Δy
The line is decreasing, so Δy is negative. The vertical change (fall) is 3 (moving down 3 units), so Δy = -3.
## Step2: Determine Δx
The horizontal change (run) is 2 (moving right 2 units), so Δx = 2.
## Step3: Calculate slope
Slope = $\frac{-3}{2}$ = -$\frac{3}{2}$

# Answer:
Rise ($\Delta y$) = -3
Run ($\Delta x$) = 2
Slope = -$\frac{3}{2}$

### Problem (4)
## Step1: Determine Δy
The line is decreasing, so Δy is negative. The vertical change (fall) is 2 (moving down 2 units), so Δy = -2.
## Step2: Determine Δx
The horizontal change (run) is 3 (moving right 3 units), so Δx = 3.
## Step3: Calculate slope
Slope = $\frac{-2}{3}$ = -$\frac{2}{3}$

# Answer:
Rise ($\Delta y$) = -2
Run ($\Delta x$) = 3
Slope = -$\frac{2}{3}$

### Problem (5)
## Step1: Determine Δy
The line is vertical, so the vertical change (Δy) can be any non - zero value (but the run is 0). Let's say we move from the bottom to the top of the line, Δy = 5 (assuming the length of the vertical line is 5 units).
## Step2: Determine Δx
The horizontal change (Δx) is 0 (since it's a vertical line, there is no horizontal movement).
## Step3: Calculate slope
A vertical line has an undefined slope because we can't divide by 0 ($\frac{\Delta y}{0}$ is undefined).

# Answer:
Rise ($\Delta y$) = 5 (or any non - zero value, depending on the length of the vertical line)
Run ($\Delta x$) = 0
Slope = Undefined

### Problem (6)
## Step1: Determine Δy
The line is decreasing, so Δy is negative. The vertical change (fall) is 4 (moving down 4 units), so Δy = -4.
## Step2: Determine Δx
The horizontal change (run) is 2 (moving right 2 units), so Δx = 2.
## Step3: Calculate slope
Slope = $\frac{-4}{2}$ = -2

# Answer:
Rise ($\Delta y$) = -4
Run ($\Delta x$) = 2
Slope = -2

### Problem (7)
## Step1: Determine Δy
The line is horizontal, so the vertical change (Δy) is 0 (there is no vertical movement).
## Step2: Determine Δx
The horizontal change (run) can be any non - zero value, say 5 (moving right 5 units).
## Step3: Calculate slope
A horizontal line has a slope of 0 because $\frac{0}{\Delta x}$ = 0 (for $\Delta x
eq0$).

# Answer:
Rise ($\Delta y$) = 0
Run ($\Delta x$) = 5 (or any non - zero value)
Slope = 0

### Problem (8)
## Step1: Determine Δy
The line is decreasing, so Δy is negative. The vertical change (fall) is 2 (moving down 2 units), so Δy = -2.
## Step2: Determine Δx
The horizontal change (run) is 3 (moving right 3 units), so Δx = 3.
## Step3: Calculate slope
Slope = $\frac{-2}{3}$ = -$\frac{2}{3}$

# Answer:
Rise ($\Delta y$) = -2
Run ($\Delta x$) = 3
Slope = -$\frac{2}{3}$

### Problem (9)
## Step1: Determine Δy
The line is increasing, so Δy is positive. The vertical change (rise) is 2 (moving up 2 units), so Δy = 2.
## Step2: Determine Δx
The horizontal change (run) is 3 (moving right 3 units), so Δx = 3.
## Step3: Calculate slope
Slope = $\frac{2}{3}$

# Answer:
Rise ($\Delta y$) = 2
Run ($\Delta x$) = 3
Slope = $\frac{2}{3}$

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QUESTION IMAGE

Question

Explanation:

Step1: Determine the change in y (Rise)

Step2: Determine the change in x (Run)

Step3: Calculate the slope

Answer:

Problem (2)

Step1: Determine Δy

Step2: Determine Δx

Step3: Calculate slope