Math / Algebra

QuestionWhat is the slope of a line. a) Paralle (b) perpendecilar to the following? 1) $3 x-4 y=2$ a) $m=$ b) $m=$ 2) $y=7 x-3$ a) $m=$ b) $m=$ 3) What does "I" mean?

Studdy Solution

STEP 1

1. We are given two linear equations and need to find the slopes of lines parallel and perpendicular to these equations.
2. Parallel lines have the same slope.
3. Perpendicular lines have slopes that are negative reciprocals of each other.
4. The symbol "I" is not defined in the context of the problem.

STEP 2

1. Find the slope of the line from the equation $3x - 4y = 2$ .
2. Determine the slopes of lines parallel and perpendicular to the line from $3x - 4y = 2$ .
3. Find the slope of the line from the equation $y = 7x - 3$ .
4. Determine the slopes of lines parallel and perpendicular to the line from $y = 7x - 3$ .
5. Address the question regarding the meaning of "I".

STEP 3

Rearrange the equation $3x - 4y = 2$ into the slope-intercept form $y = mx + b$ .
$3x - 4y = 2$
Subtract $3x$ from both sides:
$-4y = -3x + 2$
Divide every term by $-4$ to solve for $y$ :
$y = \frac{3}{4}x - \frac{1}{2}$
The slope $m$ is $\frac{3}{4}$ .

STEP 4

a) The slope of a line parallel to the given line is the same, so $m = \frac{3}{4}$ .
b) The slope of a line perpendicular to the given line is the negative reciprocal, so $m = -\frac{4}{3}$ .

STEP 5

The equation $y = 7x - 3$ is already in slope-intercept form $y = mx + b$ .
The slope $m$ is $7$ .

STEP 6

a) The slope of a line parallel to the given line is the same, so $m = 7$ .
b) The slope of a line perpendicular to the given line is the negative reciprocal, so $m = -\frac{1}{7}$ .

STEP 7

The question "What does 'I' mean?" is unclear without additional context. In mathematics, "I" could refer to the imaginary unit, identity matrix, or simply a variable, depending on the context.

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QuestionWhat is the slope of a line. a) Paralle (b) perpendecilar to the following? 1) $3 x-4 y=2$ a) $m=$ b) $m=$ 2) $y=7 x-3$ a) $m=$ b) $m=$ 3) What does "I" mean?

Studdy Solution

STEP 1

STEP 2

STEP 3

Rearrange the equation $3x - 4y = 2$ into the slope-intercept form $y = mx + b$ .
$3x - 4y = 2$
Subtract $3x$ from both sides:
$-4y = -3x + 2$
Divide every term by $-4$ to solve for $y$ :
$y = \frac{3}{4}x - \frac{1}{2}$
The slope $m$ is $\frac{3}{4}$ .

STEP 4

a) The slope of a line parallel to the given line is the same, so $m = \frac{3}{4}$ .
b) The slope of a line perpendicular to the given line is the negative reciprocal, so $m = -\frac{4}{3}$ .

STEP 5

The equation $y = 7x - 3$ is already in slope-intercept form $y = mx + b$ .
The slope $m$ is $7$ .

STEP 6

a) The slope of a line parallel to the given line is the same, so $m = 7$ .
b) The slope of a line perpendicular to the given line is the negative reciprocal, so $m = -\frac{1}{7}$ .

STEP 7

The question "What does 'I' mean?" is unclear without additional context. In mathematics, "I" could refer to the imaginary unit, identity matrix, or simply a variable, depending on the context.

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QuestionWhat is the slope of a line. a) Paralle (b) perpendecilar to the following? 1) 3x−4y=23 x-4 y=23x−4y=2 a) m=m=m= b) m=m=m= 2) y=7x−3y=7 x-3y=7x−3 a) m=m=m= b) m=m=m= 3) What does "I" mean?

Studdy Solution

STEP 1

STEP 2

STEP 3

STEP 4

a) The slope of a line parallel to the given line is the same, so m=34m = \frac{3}{4}m=43​.b) The slope of a line perpendicular to the given line is the negative reciprocal, so m=−43m = -\frac{4}{3}m=−34​.

STEP 5

The equation y=7x−3y = 7x - 3y=7x−3 is already in slope-intercept form y=mx+by = mx + by=mx+b.The slope mmm is 777.

STEP 6

a) The slope of a line parallel to the given line is the same, so m=7m = 7m=7.b) The slope of a line perpendicular to the given line is the negative reciprocal, so m=−17m = -\frac{1}{7}m=−71​.

STEP 7

The question "What does 'I' mean?" is unclear without additional context. In mathematics, "I" could refer to the imaginary unit, identity matrix, or simply a variable, depending on the context.

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 a line. a) Paralle (b) perpendecilar to the following? 1) $3 x-4 y=2$ a) $m=$ b) $m=$ 2) $y=7 x-3$ a) $m=$ b) $m=$ 3) What does "I" mean?

a) The slope of a line parallel to the given line is the same, so $m = \frac{3}{4}$ .
b) The slope of a line perpendicular to the given line is the negative reciprocal, so $m = -\frac{4}{3}$ .

The equation $y = 7x - 3$ is already in slope-intercept form $y = mx + b$ .
The slope $m$ is $7$ .

a) The slope of a line parallel to the given line is the same, so $m = 7$ .
b) The slope of a line perpendicular to the given line is the negative reciprocal, so $m = -\frac{1}{7}$ .