Math / Algebra

Question9. What is the slope of a line that is perpendicular to the graph of $y=\frac{2}{5} x-\frac{1}{3}$ ?

Studdy Solution

STEP 1

What is this asking? We need to find the slope of a line that's perpendicular to a given line. Watch out! Don't forget to flip and negate the slope of the original line!

STEP 2

1. Find the slope of the given line.
2. Find the negative reciprocal.

STEP 3

The equation of the given line is in slope-intercept form, which is $y = mx + b$ , where $m$ is the slope and $b$ is the $\boldsymbol{y}$ -intercept.

STEP 4

In our equation, $y = \frac{2}{5}x - \frac{1}{3}$ , we can see that the slope $m$ is $\frac{2}{5}$ and the $\boldsymbol{y}$ -intercept $b$ is $-\frac{1}{3}$ .
We only care about the slope right now, which is $\frac{2}{5}$ .

STEP 5

Perpendicular lines have slopes that are negative reciprocals of each other.
This means we flip the fraction and change the sign.

STEP 6

Our original slope is $\frac{2}{5}$ .
Let's flip it!
This gives us $\frac{5}{2}$ .

STEP 7

Now, let's change the sign from positive to negative.
This gives us $-\frac{5}{2}$ .

STEP 8

The slope of the perpendicular line is $-\frac{5}{2}$ .

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Question9. What is the slope of a line that is perpendicular to the graph of $y=\frac{2}{5} x-\frac{1}{3}$ ?

Studdy Solution

STEP 1

What is this asking? We need to find the slope of a line that's perpendicular to a given line. Watch out! Don't forget to flip and negate the slope of the original line!

STEP 2

1. Find the slope of the given line.
2. Find the negative reciprocal.

STEP 3

The equation of the given line is in slope-intercept form, which is $y = mx + b$ , where $m$ is the slope and $b$ is the $\boldsymbol{y}$ -intercept.

STEP 4

In our equation, $y = \frac{2}{5}x - \frac{1}{3}$ , we can see that the slope $m$ is $\frac{2}{5}$ and the $\boldsymbol{y}$ -intercept $b$ is $-\frac{1}{3}$ .
We only care about the slope right now, which is $\frac{2}{5}$ .

STEP 5

Perpendicular lines have slopes that are negative reciprocals of each other.
This means we flip the fraction and change the sign.

STEP 6

Our original slope is $\frac{2}{5}$ .
Let's flip it!
This gives us $\frac{5}{2}$ .

STEP 7

Now, let's change the sign from positive to negative.
This gives us $-\frac{5}{2}$ .

STEP 8

The slope of the perpendicular line is $-\frac{5}{2}$ .

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Question9. What is the slope of a line that is perpendicular to the graph of y=25x−13y=\frac{2}{5} x-\frac{1}{3}y=52​x−31​ ?

Studdy Solution

STEP 1

What is this asking? We need to find the slope of a line that's perpendicular to a given line. Watch out! Don't forget to flip and negate the slope of the original line!

STEP 2

1. Find the slope of the given line.2. Find the negative reciprocal.

STEP 3

The equation of the given line is in slope-intercept form, which is y=mx+by = mx + by=mx+b, where mmm is the **slope** and bbb is the y\boldsymbol{y}y**-intercept**.

STEP 4

In our equation, y=25x−13y = \frac{2}{5}x - \frac{1}{3}y=52​x−31​, we can see that the **slope** mmm is 25\frac{2}{5}52​ and the y\boldsymbol{y}y**-intercept** bbb is −13-\frac{1}{3}−31​.We only care about the **slope** right now, which is 25\frac{2}{5}52​.

STEP 5

Perpendicular lines have slopes that are **negative reciprocals** of each other.This means we flip the fraction and change the sign.

STEP 6

Our original slope is 25\frac{2}{5}52​.Let's **flip it**!This gives us 52\frac{5}{2}25​.

STEP 7

Now, let's **change the sign** from positive to negative.This gives us −52-\frac{5}{2}−25​.

STEP 8

The slope of the perpendicular line is −52-\frac{5}{2}−25​.

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Question9. What is the slope of a line that is perpendicular to the graph of $y=\frac{2}{5} x-\frac{1}{3}$ ?

1. Find the slope of the given line.
2. Find the negative reciprocal.

The equation of the given line is in slope-intercept form, which is $y = mx + b$ , where $m$ is the slope and $b$ is the $\boldsymbol{y}$ -intercept.

In our equation, $y = \frac{2}{5}x - \frac{1}{3}$ , we can see that the slope $m$ is $\frac{2}{5}$ and the $\boldsymbol{y}$ -intercept $b$ is $-\frac{1}{3}$ .
We only care about the slope right now, which is $\frac{2}{5}$ .

Perpendicular lines have slopes that are negative reciprocals of each other.
This means we flip the fraction and change the sign.

Our original slope is $\frac{2}{5}$ .
Let's flip it!
This gives us $\frac{5}{2}$ .

Now, let's change the sign from positive to negative.
This gives us $-\frac{5}{2}$ .

The slope of the perpendicular line is $-\frac{5}{2}$ .