What is the equation, in slope-intercept form, of the line that is perpendicular to the line

Mathematics

1 answer:

wolverine [178]3 years ago

8 0

Answer:

y=3/2x+1

Step-by-step explanation:

y-4= -⅔(x-6)

y-4=-⅔x+4

y=-⅔x+4+4

(equation of line 1) y= -⅔x+8 gradient= -⅔

(line 2)gradient=3/2

note* the gradients of perpendicular lines multiplied result to -1

gradient=y²-y²

x²-x¹

3 =y+2

2. x+2

multiply both sides by 2(x+2)to remove the denominators

3(x+2)=2(y+2)

3x+6=2y+4

3x+6-4=2y

3x+2=2y

divide all sides by 2

3/2x+1=y

y=3/2x+1

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In a word processing document or on a separate piece of paper, use the guide to construct a two column proof proving that lines

lisabon 2012 [21]

To enable the completion of the proof that line l is parallel to line m, a

diagram showing the lines and their common transversal is attached.

The completed two column proof is presented as follows;

Statement ${}$ Reason

1. ∠1 and ∠2 are supplementary angles ${}$ 1. Given

2. m∠1 + m∠2 = 180° ${}$ 2. Definition of supplementary ∠s

3. ∠1 and ∠3 are supplementary angles ${}$ 3. Exterior sides in opposite rays

4. m∠1 + m∠3 = 180° ${}$ 4. Definition of supplementary ∠s

5. m∠1 + m∠2 = m∠1 + m∠3 ${}$ 5. Transitive property of equality

6. m∠2 = m∠3 ${}$ 6. Subtraction property of equality

7. l ║ m ${}$ 7. Converse of alternate interior

${}$ angles postulate

Reasons:

Reason for statement 2: Supplementary angles are defined as two angles that sum up to 180°

Reason for statement 3: Two angles are supplementary if the exterior sides that form each angle are opposite rays (rays that are drawn out infinitely in opposite direction but have the same endpoint)

Statement 4: Mathematical expression of the sum of ∠1 and ∠3; Reason for statement 4 is the definition of supplementary angles

Reason for statement 5: Transitive property of equality describes the property that if a number x = y, and z = y, then x = z.

Statement 6: Subtracting m∠1 from both sides of the equation in statement 5. gives; m∠1 + m∠2 - m∠1 = m∠1 + m∠3 - m∠1 ⇒ m∠2 = m∠3. Reason for statement 6 is the subtraction property of equality

Reason for statement 7: The converse of the alternate interior angles postulate states that if the alternate interior angles formed between two lines and a common transversal are congruent, the two lines are parallel.

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