Math / Algebra

QuestionThe equation of line $t$ is $y=\frac{-9}{37} x-61$ . Line $u$ is perpendicular to $t$ . What is the slope of line $u$ ? (3), Simplify your answer and write it as a proper fraction, improper fraction, or integer. $\square$ Submit Work it out

Studdy Solution

STEP 1

1. The equation of line $t$ is given by $y = \frac{-9}{37}x - 61$ .
2. Line $u$ is perpendicular to line $t$ .
3. We are asked to find the slope of line $u$ .

STEP 2

1. Identify the slope of line $t$ .
2. Use the property of perpendicular lines to find the slope of line $u$ .
3. Simplify the slope of line $u$ if necessary.

STEP 3

Identify the slope of line $t$ .
The equation of line $t$ is in the slope-intercept form $y = mx + b$ , where $m$ is the slope. Therefore, the slope of line $t$ is $\frac{-9}{37}$ .

STEP 4

Use the property of perpendicular lines to find the slope of line $u$ .
The slopes of two perpendicular lines are negative reciprocals of each other. Thus, if the slope of line $t$ is $\frac{-9}{37}$ , then the slope of line $u$ is the negative reciprocal of $\frac{-9}{37}$ .

STEP 5

Calculate the negative reciprocal of $\frac{-9}{37}$ .
The reciprocal of $\frac{-9}{37}$ is $\frac{37}{-9}$ . The negative reciprocal is $\frac{37}{9}$ .

STEP 6

Simplify the slope of line $u$ if necessary.
The slope $\frac{37}{9}$ is already in its simplest form as an improper fraction.
The slope of line $u$ is:
$\boxed{\frac{37}{9}}$

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QuestionThe equation of line $t$ is $y=\frac{-9}{37} x-61$ . Line $u$ is perpendicular to $t$ . What is the slope of line $u$ ? (3), Simplify your answer and write it as a proper fraction, improper fraction, or integer. $\square$ Submit Work it out

Studdy Solution

STEP 1

1. The equation of line $t$ is given by $y = \frac{-9}{37}x - 61$ .
2. Line $u$ is perpendicular to line $t$ .
3. We are asked to find the slope of line $u$ .

STEP 2

1. Identify the slope of line $t$ .
2. Use the property of perpendicular lines to find the slope of line $u$ .
3. Simplify the slope of line $u$ if necessary.

STEP 3

Identify the slope of line $t$ .
The equation of line $t$ is in the slope-intercept form $y = mx + b$ , where $m$ is the slope. Therefore, the slope of line $t$ is $\frac{-9}{37}$ .

STEP 4

Use the property of perpendicular lines to find the slope of line $u$ .
The slopes of two perpendicular lines are negative reciprocals of each other. Thus, if the slope of line $t$ is $\frac{-9}{37}$ , then the slope of line $u$ is the negative reciprocal of $\frac{-9}{37}$ .

STEP 5

Calculate the negative reciprocal of $\frac{-9}{37}$ .
The reciprocal of $\frac{-9}{37}$ is $\frac{37}{-9}$ . The negative reciprocal is $\frac{37}{9}$ .

STEP 6

Simplify the slope of line $u$ if necessary.
The slope $\frac{37}{9}$ is already in its simplest form as an improper fraction.
The slope of line $u$ is:
$\boxed{\frac{37}{9}}$

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QuestionThe equation of line ttt is y=−937x−61y=\frac{-9}{37} x-61y=37−9​x−61. Line uuu is perpendicular to ttt. What is the slope of line uuu ? (3), Simplify your answer and write it as a proper fraction, improper fraction, or integer. □\square□ Submit Work it out

Studdy Solution

STEP 1

1. The equation of line t t t is given by y=−937x−61 y = \frac{-9}{37}x - 61 y=37−9​x−61.2. Line u u u is perpendicular to line t t t.3. We are asked to find the slope of line u u u.

STEP 2

1. Identify the slope of line t t t.2. Use the property of perpendicular lines to find the slope of line u u u.3. Simplify the slope of line u u u if necessary.

STEP 3

Identify the slope of line t t t.The equation of line t t t is in the slope-intercept form y=mx+b y = mx + b y=mx+b, where m m m is the slope. Therefore, the slope of line t t t is −937 \frac{-9}{37} 37−9​.

STEP 4

STEP 5

Calculate the negative reciprocal of −937 \frac{-9}{37} 37−9​.The reciprocal of −937 \frac{-9}{37} 37−9​ is 37−9 \frac{37}{-9} −937​. The negative reciprocal is 379 \frac{37}{9} 937​.

STEP 6

Simplify the slope of line u u u if necessary.The slope 379 \frac{37}{9} 937​ is already in its simplest form as an improper fraction.The slope of line u u u is:379 \boxed{\frac{37}{9}} 937​​

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QuestionThe equation of line $t$ is $y=\frac{-9}{37} x-61$ . Line $u$ is perpendicular to $t$ . What is the slope of line $u$ ? (3), Simplify your answer and write it as a proper fraction, improper fraction, or integer. $\square$ Submit Work it out

1. The equation of line $t$ is given by $y = \frac{-9}{37}x - 61$ .
2. Line $u$ is perpendicular to line $t$ .
3. We are asked to find the slope of line $u$ .

1. Identify the slope of line $t$ .
2. Use the property of perpendicular lines to find the slope of line $u$ .
3. Simplify the slope of line $u$ if necessary.

Identify the slope of line $t$ .
The equation of line $t$ is in the slope-intercept form $y = mx + b$ , where $m$ is the slope. Therefore, the slope of line $t$ is $\frac{-9}{37}$ .

Calculate the negative reciprocal of $\frac{-9}{37}$ .
The reciprocal of $\frac{-9}{37}$ is $\frac{37}{-9}$ . The negative reciprocal is $\frac{37}{9}$ .

Simplify the slope of line $u$ if necessary.
The slope $\frac{37}{9}$ is already in its simplest form as an improper fraction.
The slope of line $u$ is:
$\boxed{\frac{37}{9}}$