Math / Algebra

Question(3) Line $g$ has a slope of $\frac{40}{77}$ . Line $h$ is perpendicular to $g$ . What is the slope of line $h$ ? $\square$ Submit If Work it out Not feeling ready yet? These can help:

Studdy Solution

STEP 1

1. Line $g$ has a slope $m_g = \frac{40}{77}$ .
2. Line $h$ is perpendicular to line $g$ .
3. The slope of line $h$ can be found using the relationship between perpendicular lines.

STEP 2

1. Understand the relationship between the slopes of perpendicular lines.
2. Calculate the slope of line $h$ using the perpendicular slope relationship.

STEP 3

The slopes of two perpendicular lines are negative reciprocals of each other. This means if one line has a slope $m$ , the perpendicular line will have a slope of $-\frac{1}{m}$ .

STEP 4

Given the slope of line $g$ is $m_g = \frac{40}{77}$ , the slope of line $h$ , which is perpendicular to $g$ , is calculated as follows:
$m_h = -\frac{1}{m_g} = -\frac{1}{\frac{40}{77}}$

STEP 5

Simplify the expression for $m_h$ :
$m_h = -\frac{77}{40}$
The slope of line $h$ is:
$\boxed{-\frac{77}{40}}$

Was this helpful?

Question(3) Line $g$ has a slope of $\frac{40}{77}$ . Line $h$ is perpendicular to $g$ . What is the slope of line $h$ ? $\square$ Submit If Work it out Not feeling ready yet? These can help:

Studdy Solution

STEP 1

1. Line $g$ has a slope $m_g = \frac{40}{77}$ .
2. Line $h$ is perpendicular to line $g$ .
3. The slope of line $h$ can be found using the relationship between perpendicular lines.

STEP 2

1. Understand the relationship between the slopes of perpendicular lines.
2. Calculate the slope of line $h$ using the perpendicular slope relationship.

STEP 3

The slopes of two perpendicular lines are negative reciprocals of each other. This means if one line has a slope $m$ , the perpendicular line will have a slope of $-\frac{1}{m}$ .

STEP 4

Given the slope of line $g$ is $m_g = \frac{40}{77}$ , the slope of line $h$ , which is perpendicular to $g$ , is calculated as follows:
$m_h = -\frac{1}{m_g} = -\frac{1}{\frac{40}{77}}$

STEP 5

Simplify the expression for $m_h$ :
$m_h = -\frac{77}{40}$
The slope of line $h$ is:
$\boxed{-\frac{77}{40}}$

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.

Question(3) Line ggg has a slope of 4077\frac{40}{77}7740​. Line hhh is perpendicular to ggg. What is the slope of line hhh ? □\square□ Submit If Work it out Not feeling ready yet? These can help:

Studdy Solution

STEP 1

1. Line g g g has a slope mg=4077 m_g = \frac{40}{77} mg​=7740​.2. Line h h h is perpendicular to line g g g.3. The slope of line h h h can be found using the relationship between perpendicular lines.

STEP 2

1. Understand the relationship between the slopes of perpendicular lines.2. Calculate the slope of line h h h using the perpendicular slope relationship.

STEP 3

The slopes of two perpendicular lines are negative reciprocals of each other. This means if one line has a slope m m m, the perpendicular line will have a slope of −1m -\frac{1}{m} −m1​.

STEP 4

Given the slope of line g g g is mg=4077 m_g = \frac{40}{77} mg​=7740​, the slope of line h h h, which is perpendicular to g g g, is calculated as follows:mh=−1mg=−14077 m_h = -\frac{1}{m_g} = -\frac{1}{\frac{40}{77}} mh​=−mg​1​=−7740​1​

STEP 5

Simplify the expression for mh m_h mh​:mh=−7740 m_h = -\frac{77}{40} mh​=−4077​ The slope of line h h h is:−7740 \boxed{-\frac{77}{40}} −4077​​

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.

Question(3) Line $g$ has a slope of $\frac{40}{77}$ . Line $h$ is perpendicular to $g$ . What is the slope of line $h$ ? $\square$ Submit If Work it out Not feeling ready yet? These can help:

1. Line $g$ has a slope $m_g = \frac{40}{77}$ .
2. Line $h$ is perpendicular to line $g$ .
3. The slope of line $h$ can be found using the relationship between perpendicular lines.

1. Understand the relationship between the slopes of perpendicular lines.
2. Calculate the slope of line $h$ using the perpendicular slope relationship.

The slopes of two perpendicular lines are negative reciprocals of each other. This means if one line has a slope $m$ , the perpendicular line will have a slope of $-\frac{1}{m}$ .

Given the slope of line $g$ is $m_g = \frac{40}{77}$ , the slope of line $h$ , which is perpendicular to $g$ , is calculated as follows:
$m_h = -\frac{1}{m_g} = -\frac{1}{\frac{40}{77}}$

Simplify the expression for $m_h$ :
$m_h = -\frac{77}{40}$
The slope of line $h$ is:
$\boxed{-\frac{77}{40}}$