Math / Algebra

QuestionQuestion Show Examples
Find the slope of a line perpendicular to the line whose equation is $3 x+y=8$ . Fully simplify your answer.
Answer Attempt 1 out of 2

Studdy Solution

STEP 1

What is this asking? We need to find the slope of a line that's perpendicular to another line, which is described by the equation $3x + y = 8$ . Watch out! Don't mix up the slope of the given line with the slope of the perpendicular line!

STEP 2

1. Rewrite the equation
2. Find the slope
3. Perpendicular slope

STEP 3

Let's rewrite the equation $3x + y = 8$ into slope-intercept form, which is $y = mx + b$ .
This form is super useful because $m$ represents the slope and $b$ represents the y-intercept.

STEP 4

To get there, we want to isolate $y$ .
We can do this by subtracting $3x$ from both sides of the equation: $3x + y - 3x = 8 - 3x$ $y = -3x + 8$

STEP 5

Now, our equation is in slope-intercept form!
Remember, the slope is the coefficient of $x$ .
In our equation, $y = -3x + 8$ , the coefficient of $x$ is $-3$ .

STEP 6

So, the slope of the given line is $-3$ .
We'll call this $m_1 = -3$ .

STEP 7

We want the slope of a line perpendicular to this one.
Perpendicular lines have slopes that are negative reciprocals of each other.
This means if we flip the fraction and change the sign, we get the perpendicular slope.

STEP 8

Let's call the slope of the perpendicular line $m_2$ .
To find $m_2$ , we take the negative reciprocal of $m_1$ : $m_2 = -\frac{1}{m_1}$ $m_2 = -\frac{1}{-3}$ $m_2 = \frac{1}{3}$

STEP 9

The slope of the line perpendicular to $3x + y = 8$ is $\frac{1}{3}$ .

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QuestionQuestion Show Examples
Find the slope of a line perpendicular to the line whose equation is $3 x+y=8$ . Fully simplify your answer.
Answer Attempt 1 out of 2

Studdy Solution

STEP 1

What is this asking? We need to find the slope of a line that's perpendicular to another line, which is described by the equation $3x + y = 8$ . Watch out! Don't mix up the slope of the given line with the slope of the perpendicular line!

STEP 2

1. Rewrite the equation
2. Find the slope
3. Perpendicular slope

STEP 3

Let's rewrite the equation $3x + y = 8$ into slope-intercept form, which is $y = mx + b$ .
This form is super useful because $m$ represents the slope and $b$ represents the y-intercept.

STEP 4

To get there, we want to isolate $y$ .
We can do this by subtracting $3x$ from both sides of the equation: $3x + y - 3x = 8 - 3x$ $y = -3x + 8$

STEP 5

Now, our equation is in slope-intercept form!
Remember, the slope is the coefficient of $x$ .
In our equation, $y = -3x + 8$ , the coefficient of $x$ is $-3$ .

STEP 6

So, the slope of the given line is $-3$ .
We'll call this $m_1 = -3$ .

STEP 7

We want the slope of a line perpendicular to this one.
Perpendicular lines have slopes that are negative reciprocals of each other.
This means if we flip the fraction and change the sign, we get the perpendicular slope.

STEP 8

Let's call the slope of the perpendicular line $m_2$ .
To find $m_2$ , we take the negative reciprocal of $m_1$ : $m_2 = -\frac{1}{m_1}$ $m_2 = -\frac{1}{-3}$ $m_2 = \frac{1}{3}$

STEP 9

The slope of the line perpendicular to $3x + y = 8$ is $\frac{1}{3}$ .

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QuestionQuestion Show ExamplesFind the slope of a line perpendicular to the line whose equation is 3x+y=83 x+y=83x+y=8. Fully simplify your answer.Answer Attempt 1 out of 2

Studdy Solution

STEP 1

What is this asking? We need to find the slope of a line that's perpendicular to another line, which is described by the equation 3x+y=83x + y = 83x+y=8. Watch out! Don't mix up the slope of the *given* line with the slope of the *perpendicular* line!

STEP 2

1. Rewrite the equation2. Find the slope3. Perpendicular slope

STEP 3

Let's **rewrite** the equation 3x+y=83x + y = 83x+y=8 into slope-intercept form, which is y=mx+by = mx + by=mx+b.This form is super useful because mmm represents the **slope** and bbb represents the **y-intercept**.

STEP 4

To get there, we want to **isolate** yyy.We can do this by subtracting 3x3x3x from both sides of the equation: 3x+y−3x=8−3x3x + y - 3x = 8 - 3x3x+y−3x=8−3x y=−3x+8y = -3x + 8y=−3x+8

STEP 5

Now, our equation is in slope-intercept form!Remember, the **slope** is the coefficient of xxx.In our equation, y=−3x+8y = -3x + 8y=−3x+8, the coefficient of xxx is −3-3−3.

STEP 6

So, the slope of the *given* line is −3-3−3.We'll call this m1=−3m_1 = -3m1​=−3.

STEP 7

We want the slope of a line *perpendicular* to this one.Perpendicular lines have slopes that are **negative reciprocals** of each other.This means if we flip the fraction and change the sign, we get the perpendicular slope.

STEP 8

Let's call the slope of the perpendicular line m2m_2m2​.To find m2m_2m2​, we take the negative reciprocal of m1m_1m1​: m2=−1m1m_2 = -\frac{1}{m_1}m2​=−m1​1​ m2=−1−3m_2 = -\frac{1}{-3}m2​=−−31​m2=13m_2 = \frac{1}{3}m2​=31​

STEP 9

The slope of the line perpendicular to 3x+y=83x + y = 83x+y=8 is 13\frac{1}{3}31​.

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QuestionQuestion Show Examples
Find the slope of a line perpendicular to the line whose equation is $3 x+y=8$ . Fully simplify your answer.
Answer Attempt 1 out of 2

What is this asking? We need to find the slope of a line that's perpendicular to another line, which is described by the equation $3x + y = 8$ . Watch out! Don't mix up the slope of the given line with the slope of the perpendicular line!

1. Rewrite the equation
2. Find the slope
3. Perpendicular slope

Let's rewrite the equation $3x + y = 8$ into slope-intercept form, which is $y = mx + b$ .
This form is super useful because $m$ represents the slope and $b$ represents the y-intercept.

To get there, we want to isolate $y$ .
We can do this by subtracting $3x$ from both sides of the equation: $3x + y - 3x = 8 - 3x$ $y = -3x + 8$

Now, our equation is in slope-intercept form!
Remember, the slope is the coefficient of $x$ .
In our equation, $y = -3x + 8$ , the coefficient of $x$ is $-3$ .

So, the slope of the given line is $-3$ .
We'll call this $m_1 = -3$ .

We want the slope of a line perpendicular to this one.
Perpendicular lines have slopes that are negative reciprocals of each other.
This means if we flip the fraction and change the sign, we get the perpendicular slope.

Let's call the slope of the perpendicular line $m_2$ .
To find $m_2$ , we take the negative reciprocal of $m_1$ : $m_2 = -\frac{1}{m_1}$ $m_2 = -\frac{1}{-3}$ $m_2 = \frac{1}{3}$

The slope of the line perpendicular to $3x + y = 8$ is $\frac{1}{3}$ .