Math / Algebra

QuestionWhat is the slope of the line that passes through the points $(-9, 0)$ and $(-17, 4)$ ? Write your answer in simplest form. Answer Attempt 1 out of 2

Studdy Solution

STEP 1

What is this asking? We need to find the steepness of a line connecting two points, which is called the slope! Watch out! Don't mix up the $x$ and $y$ coordinates!
Also, remember the order matters in the slope formula.

STEP 2

1. Label the points
2. Apply the slope formula

STEP 3

Let's label our two points to keep things organized.
We'll call $(-9, 0)$ point 1, so $x_1 = -9$ and $y_1 = 0$ .
And we'll call $(-17, 4)$ point 2, so $x_2 = -17$ and $y_2 = 4$ .
See how neat and tidy that is?

STEP 4

The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$ , where $m$ represents the slope.
It's basically the change in $y$ divided by the change in $x$ .
Think "rise over run"!

STEP 5

Let's plug in our values: $m = \frac{4 - 0}{-17 - (-9)}$ .
Notice how we're subtracting a negative number in the denominator.
That's the same as adding!

STEP 6

So, $m = \frac{4}{-17 + 9}$ .
This simplifies to $m = \frac{4}{-8}$ .

STEP 7

We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which is 4.
So, $\frac{4}{-8} = \frac{4 \div 4}{-8 \div 4} = \frac{1}{-2}$ .

STEP 8

Our final simplified slope is $-\frac{1}{2}$ .

STEP 9

The slope of the line passing through the points $(-9, 0)$ and $(-17, 4)$ is $-\frac{1}{2}$ .

Was this helpful?

QuestionWhat is the slope of the line that passes through the points $(-9, 0)$ and $(-17, 4)$ ? Write your answer in simplest form. Answer Attempt 1 out of 2

Studdy Solution

STEP 1

What is this asking? We need to find the steepness of a line connecting two points, which is called the slope! Watch out! Don't mix up the $x$ and $y$ coordinates!
Also, remember the order matters in the slope formula.

STEP 2

1. Label the points
2. Apply the slope formula

STEP 3

Let's label our two points to keep things organized.
We'll call $(-9, 0)$ point 1, so $x_1 = -9$ and $y_1 = 0$ .
And we'll call $(-17, 4)$ point 2, so $x_2 = -17$ and $y_2 = 4$ .
See how neat and tidy that is?

STEP 4

The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$ , where $m$ represents the slope.
It's basically the change in $y$ divided by the change in $x$ .
Think "rise over run"!

STEP 5

Let's plug in our values: $m = \frac{4 - 0}{-17 - (-9)}$ .
Notice how we're subtracting a negative number in the denominator.
That's the same as adding!

STEP 6

So, $m = \frac{4}{-17 + 9}$ .
This simplifies to $m = \frac{4}{-8}$ .

STEP 7

We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which is 4.
So, $\frac{4}{-8} = \frac{4 \div 4}{-8 \div 4} = \frac{1}{-2}$ .

STEP 8

Our final simplified slope is $-\frac{1}{2}$ .

STEP 9

The slope of the line passing through the points $(-9, 0)$ and $(-17, 4)$ is $-\frac{1}{2}$ .

Get Studdy

Studdy solves anything!

Start learning now

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

QuestionWhat is the slope of the line that passes through the points (−9,0)(-9, 0)(−9,0) and (−17,4)(-17, 4)(−17,4)? Write your answer in simplest form. Answer Attempt 1 out of 2

Studdy Solution

STEP 1

What is this asking? We need to find the steepness of a line connecting two points, which is called the slope! Watch out! Don't mix up the xxx and yyy coordinates!Also, remember the order matters in the slope formula.

STEP 2

1. Label the points2. Apply the slope formula

STEP 3

Let's **label** our two points to keep things organized.We'll call (−9,0)(-9, 0)(−9,0) point 1, so x1=−9x_1 = -9x1​=−9 and y1=0y_1 = 0y1​=0.And we'll call (−17,4)(-17, 4)(−17,4) point 2, so x2=−17x_2 = -17x2​=−17 and y2=4y_2 = 4y2​=4.See how neat and tidy that is?

STEP 4

The **slope formula** is m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}m=x2​−x1​y2​−y1​​, where mmm represents the slope.It's basically the change in yyy divided by the change in xxx.Think "rise over run"!

STEP 5

Let's **plug in** our values: m=4−0−17−(−9)m = \frac{4 - 0}{-17 - (-9)}m=−17−(−9)4−0​.Notice how we're subtracting a negative number in the denominator.That's the same as adding!

STEP 6

So, m=4−17+9m = \frac{4}{-17 + 9}m=−17+94​.This simplifies to m=4−8m = \frac{4}{-8}m=−84​.

STEP 7

We can **simplify** this fraction by dividing both the numerator and denominator by their greatest common factor, which is **4**.So, 4−8=4÷4−8÷4=1−2\frac{4}{-8} = \frac{4 \div 4}{-8 \div 4} = \frac{1}{-2}−84​=−8÷44÷4​=−21​.

STEP 8

Our **final simplified slope** is −12-\frac{1}{2}−21​.

STEP 9

The slope of the line passing through the points (−9,0)(-9, 0)(−9,0) and (−17,4)(-17, 4)(−17,4) is −12-\frac{1}{2}−21​.

Get Studdy

Studdy solves anything!

Start learning now

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

QuestionWhat is the slope of the line that passes through the points $(-9, 0)$ and $(-17, 4)$ ? Write your answer in simplest form. Answer Attempt 1 out of 2

What is this asking? We need to find the steepness of a line connecting two points, which is called the slope! Watch out! Don't mix up the $x$ and $y$ coordinates!
Also, remember the order matters in the slope formula.

1. Label the points
2. Apply the slope formula

Let's label our two points to keep things organized.
We'll call $(-9, 0)$ point 1, so $x_1 = -9$ and $y_1 = 0$ .
And we'll call $(-17, 4)$ point 2, so $x_2 = -17$ and $y_2 = 4$ .
See how neat and tidy that is?

The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$ , where $m$ represents the slope.
It's basically the change in $y$ divided by the change in $x$ .
Think "rise over run"!

Let's plug in our values: $m = \frac{4 - 0}{-17 - (-9)}$ .
Notice how we're subtracting a negative number in the denominator.
That's the same as adding!

So, $m = \frac{4}{-17 + 9}$ .
This simplifies to $m = \frac{4}{-8}$ .

We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which is 4.
So, $\frac{4}{-8} = \frac{4 \div 4}{-8 \div 4} = \frac{1}{-2}$ .

Our final simplified slope is $-\frac{1}{2}$ .

The slope of the line passing through the points $(-9, 0)$ and $(-17, 4)$ is $-\frac{1}{2}$ .