Math / Geometry

QuestionFind the slope of the line graphed below.

Studdy Solution

STEP 1

What is this asking? We need to find how steep the line is! Watch out! Don't mix up the $x$ and $y$ coordinates!

STEP 2

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

STEP 3

The rise is the change in the $y$ values between the two points.
We're looking at how much the line goes up (or down).
Our points are $(-3, -2)$ and $(0, 3)$ .
The $y$ values are $-2$ and $3$ .

STEP 4

To find the change, we subtract the initial $y$ value from the final $y$ value.
So, that's $3 - (-2)$ .
Remember subtracting a negative is the same as adding a positive!

STEP 5

So, $3 - (-2) = 3 + 2 = \mathbf{5}$ .
Our rise is 5!

STEP 6

The run is the change in the $x$ values between the two points.
We're looking at how much the line goes sideways.

STEP 7

Our $x$ values are $-3$ and $0$ .
To find the change, we subtract the initial $x$ value from the final $x$ value: $0 - (-3)$ .
Again, subtracting a negative is adding a positive!

STEP 8

So, $0 - (-3) = 0 + 3 = \mathbf{3}$ .
Our run is 3!

STEP 9

The slope of a line is the rise divided by the run.
It tells us how much the line goes up for every unit it goes sideways.

STEP 10

We found our rise was 5 and our run was 3.
So, our slope is $\frac{5}{3}$ .

STEP 11

The slope of the line is $\frac{5}{3}$ !

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QuestionFind the slope of the line graphed below.

Studdy Solution

STEP 1

What is this asking? We need to find how steep the line is! Watch out! Don't mix up the $x$ and $y$ coordinates!

STEP 2

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

STEP 3

The rise is the change in the $y$ values between the two points.
We're looking at how much the line goes up (or down).
Our points are $(-3, -2)$ and $(0, 3)$ .
The $y$ values are $-2$ and $3$ .

STEP 4

To find the change, we subtract the initial $y$ value from the final $y$ value.
So, that's $3 - (-2)$ .
Remember subtracting a negative is the same as adding a positive!

STEP 5

So, $3 - (-2) = 3 + 2 = \mathbf{5}$ .
Our rise is 5!

STEP 6

The run is the change in the $x$ values between the two points.
We're looking at how much the line goes sideways.

STEP 7

Our $x$ values are $-3$ and $0$ .
To find the change, we subtract the initial $x$ value from the final $x$ value: $0 - (-3)$ .
Again, subtracting a negative is adding a positive!

STEP 8

So, $0 - (-3) = 0 + 3 = \mathbf{3}$ .
Our run is 3!

STEP 9

The slope of a line is the rise divided by the run.
It tells us how much the line goes up for every unit it goes sideways.

STEP 10

We found our rise was 5 and our run was 3.
So, our slope is $\frac{5}{3}$ .

STEP 11

The slope of the line is $\frac{5}{3}$ !

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QuestionFind the slope of the line graphed below.

Studdy Solution

STEP 1

What is this asking? We need to find how steep the line is! Watch out! Don't mix up the xxx and yyy coordinates!

STEP 2

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

STEP 3

The **rise** is the change in the yyy values between the two points.We're looking at how much the line goes *up* (or *down*).Our points are (−3,−2)(-3, -2)(−3,−2) and (0,3)(0, 3)(0,3).The yyy values are −2-2−2 and 333.

STEP 4

To find the change, we subtract the **initial** yyy value from the **final** yyy value.So, that's 3−(−2)3 - (-2)3−(−2).Remember subtracting a negative is the same as adding a positive!

STEP 5

So, 3−(−2)=3+2=53 - (-2) = 3 + 2 = \mathbf{5}3−(−2)=3+2=5.Our **rise** is **5**!

STEP 6

The **run** is the change in the xxx values between the two points.We're looking at how much the line goes *sideways*.

STEP 7

Our xxx values are −3-3−3 and 000.To find the change, we subtract the **initial** xxx value from the **final** xxx value: 0−(−3)0 - (-3)0−(−3).Again, subtracting a negative is adding a positive!

STEP 8

So, 0−(−3)=0+3=30 - (-3) = 0 + 3 = \mathbf{3}0−(−3)=0+3=3.Our **run** is **3**!

STEP 9

The **slope** of a line is the **rise** divided by the **run**.It tells us how much the line goes up for every unit it goes sideways.

STEP 10

We found our **rise** was **5** and our **run** was **3**.So, our slope is 53\frac{5}{3}35​.

STEP 11

The slope of the line is 53\frac{5}{3}35​!

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What is this asking? We need to find how steep the line is! Watch out! Don't mix up the $x$ and $y$ coordinates!

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

The rise is the change in the $y$ values between the two points.
We're looking at how much the line goes up (or down).
Our points are $(-3, -2)$ and $(0, 3)$ .
The $y$ values are $-2$ and $3$ .

To find the change, we subtract the initial $y$ value from the final $y$ value.
So, that's $3 - (-2)$ .
Remember subtracting a negative is the same as adding a positive!

So, $3 - (-2) = 3 + 2 = \mathbf{5}$ .
Our rise is 5!

The run is the change in the $x$ values between the two points.
We're looking at how much the line goes sideways.

Our $x$ values are $-3$ and $0$ .
To find the change, we subtract the initial $x$ value from the final $x$ value: $0 - (-3)$ .
Again, subtracting a negative is adding a positive!

So, $0 - (-3) = 0 + 3 = \mathbf{3}$ .
Our run is 3!

The slope of a line is the rise divided by the run.
It tells us how much the line goes up for every unit it goes sideways.

We found our rise was 5 and our run was 3.
So, our slope is $\frac{5}{3}$ .

The slope of the line is $\frac{5}{3}$ !