Math / Geometry

Question2 Theme Transition Slideshow COUNTING RISE OVER RUN To determine the slope of the line, count and record the rise over run! 10 801 9 2 -10-8-6-4-2 -2 4 -6 RISE: 2 4 6 8 10 RUN: CO -10 Open in a

Studdy Solution

STEP 1

What is this asking? We need to find the slope of the line shown on the graph, using the "rise over run" method. Watch out! Be careful with the signs of the rise and run!
A downward movement is a negative rise, and a leftward movement is a negative run.

STEP 2

1. Find the rise.
2. Find the run.
3. Calculate the slope.

STEP 3

Alright, let's start with the rise!
This is the vertical change between the two points.
We're going from a y-value of $8$ down to a y-value of $-2$ .

STEP 4

Think of it like this: We're starting at $8$ on the y-axis and moving down to $-2$ .
How much do we move?
Well, that's $8$ down to $0$ , and then another $2$ down to $-2$ .
That's a total downward movement of $8 + 2 = 10$ .
Since we're moving downwards, our rise is actually $-10$ .

STEP 5

Now for the run!
This is the horizontal change between the two points.
We're starting at an x-value of $-8$ and going to an x-value of $2$ .

STEP 6

Visualize it: We're moving from $-8$ to $2$ on the x-axis.
That's like moving $8$ units to get to $0$ , and then $2$ more units to get to $2$ .
So, we're moving a total of $8 + 2 = 10$ units to the right.
Our run is $+10$ .

STEP 7

Remember, the slope is just the rise divided by the run.
We found our rise to be $-10$ and our run to be $10$ .

STEP 8

So, our slope is: $\frac{\text{rise}}{\text{run}} = \frac{-10}{10}$

STEP 9

We can simplify this fraction by dividing both the numerator and denominator by $10$ : $\frac{-10}{10} = \frac{-10 \cdot 1}{10 \cdot 1} = \frac{-1 \cdot 10}{1 \cdot 10} = \frac{-1}{1} \cdot \frac{10}{10} = \frac{-1}{1} \cdot 1 = -1$ So, our final slope is $-1$ !

STEP 10

The slope of the line is $-1$ .

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Question2 Theme Transition Slideshow COUNTING RISE OVER RUN To determine the slope of the line, count and record the rise over run! 10 801 9 2 -10-8-6-4-2 -2 4 -6 RISE: 2 4 6 8 10 RUN: CO -10 Open in a

Studdy Solution

STEP 1

What is this asking? We need to find the slope of the line shown on the graph, using the "rise over run" method. Watch out! Be careful with the signs of the rise and run!
A downward movement is a negative rise, and a leftward movement is a negative run.

STEP 2

1. Find the rise.
2. Find the run.
3. Calculate the slope.

STEP 3

Alright, let's start with the rise!
This is the vertical change between the two points.
We're going from a y-value of $8$ down to a y-value of $-2$ .

STEP 4

Think of it like this: We're starting at $8$ on the y-axis and moving down to $-2$ .
How much do we move?
Well, that's $8$ down to $0$ , and then another $2$ down to $-2$ .
That's a total downward movement of $8 + 2 = 10$ .
Since we're moving downwards, our rise is actually $-10$ .

STEP 5

Now for the run!
This is the horizontal change between the two points.
We're starting at an x-value of $-8$ and going to an x-value of $2$ .

STEP 6

Visualize it: We're moving from $-8$ to $2$ on the x-axis.
That's like moving $8$ units to get to $0$ , and then $2$ more units to get to $2$ .
So, we're moving a total of $8 + 2 = 10$ units to the right.
Our run is $+10$ .

STEP 7

Remember, the slope is just the rise divided by the run.
We found our rise to be $-10$ and our run to be $10$ .

STEP 8

So, our slope is: $\frac{\text{rise}}{\text{run}} = \frac{-10}{10}$

STEP 9

We can simplify this fraction by dividing both the numerator and denominator by $10$ : $\frac{-10}{10} = \frac{-10 \cdot 1}{10 \cdot 1} = \frac{-1 \cdot 10}{1 \cdot 10} = \frac{-1}{1} \cdot \frac{10}{10} = \frac{-1}{1} \cdot 1 = -1$ So, our final slope is $-1$ !

STEP 10

The slope of the line is $-1$ .

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Question2 Theme Transition Slideshow COUNTING RISE OVER RUN To determine the slope of the line, count and record the rise over run! 10 801 9 2 -10-8-6-4-2 -2 4 -6 RISE: 2 4 6 8 10 RUN: CO -10 Open in a

Studdy Solution

STEP 1

What is this asking? We need to find the slope of the line shown on the graph, using the "rise over run" method. Watch out! Be careful with the signs of the rise and run!A downward movement is a negative rise, and a leftward movement is a negative run.

STEP 2

1. Find the rise.2. Find the run.3. Calculate the slope.

STEP 3

Alright, let's **start** with the **rise**!This is the vertical change between the two points.We're going from a y-value of 888 down to a y-value of −2-2−2.

STEP 4

STEP 5

Now for the **run**!This is the horizontal change between the two points.We're starting at an x-value of −8-8−8 and going to an x-value of 222.

STEP 6

Visualize it: We're moving from −8-8−8 to 222 on the x-axis.That's like moving 888 units to get to 000, and then 222 more units to get to 222.So, we're moving a total of 8+2=108 + 2 = 108+2=10 units to the *right*.Our **run** is +10+10+10.

STEP 7

Remember, the **slope** is just the **rise** divided by the **run**.We found our **rise** to be −10-10−10 and our **run** to be 101010.

STEP 8

So, our **slope** is: riserun=−1010 \frac{\text{rise}}{\text{run}} = \frac{-10}{10} runrise​=10−10​

STEP 9

STEP 10

The slope of the line is −1-1−1.

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Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

What is this asking? We need to find the slope of the line shown on the graph, using the "rise over run" method. Watch out! Be careful with the signs of the rise and run!
A downward movement is a negative rise, and a leftward movement is a negative run.

1. Find the rise.
2. Find the run.
3. Calculate the slope.

Alright, let's start with the rise!
This is the vertical change between the two points.
We're going from a y-value of $8$ down to a y-value of $-2$ .

Now for the run!
This is the horizontal change between the two points.
We're starting at an x-value of $-8$ and going to an x-value of $2$ .

Visualize it: We're moving from $-8$ to $2$ on the x-axis.
That's like moving $8$ units to get to $0$ , and then $2$ more units to get to $2$ .
So, we're moving a total of $8 + 2 = 10$ units to the right.
Our run is $+10$ .

Remember, the slope is just the rise divided by the run.
We found our rise to be $-10$ and our run to be $10$ .

So, our slope is: $\frac{\text{rise}}{\text{run}} = \frac{-10}{10}$

The slope of the line is $-1$ .