Lines a b c and d are shown below. Which lines are parallel? Which line are perpendicular? Explain and jutsify your answer using slopes
Answers
Answer:
Lines A and C are parallel
Lines B and D are perpendicular
Step-by-step explanation:
Given
See attachment for lines A to D
Required
Determine the parallel and perpendicular lines
To start with, we calculate the slope of each line.
Line A
The points on line A are:
[tex](x_1,y_1) = (3,-4)[/tex]
[tex](x_2,y_2) = (-1,2)[/tex]
Calculate the slope (m)
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{2 - (-4)}{-1 - 3}[/tex]
[tex]m = \frac{2 +4}{-4}[/tex]
[tex]m = \frac{6}{-4}[/tex]
[tex]m_1 = -\frac{3}{2}[/tex]
Line B
[tex](x_1,y_1) = (-1,8)[/tex]
[tex](x_2,y_2) = (2,6)[/tex]
Calculate the slope (m)
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{6 - 8}{2 -(-1)}[/tex]
[tex]m = \frac{-2}{2 +1}[/tex]
[tex]m_2 = -\frac{2}{3}[/tex]
Line C
[tex]y - 9 = -\frac{3}{2}(x + 8)[/tex]
Open bracket
[tex]y - 9 = -\frac{3}{2}x -\frac{3}{2}* 8[/tex]
[tex]y - 9 = -\frac{3}{2}x -3* 4[/tex]
[tex]y - 9 = -\frac{3}{2}x -12[/tex]
Make y the subject
[tex]y = -\frac{3}{2}x -12+9[/tex]
[tex]y = -\frac{3}{2}x -3[/tex]
The slope intercept of an equation is: [tex]y = mx + b[/tex]
Where
[tex]m = slope[/tex]
By comparison:
[tex]m_3 = -\frac{3}{2}[/tex]
Line D
[tex]12x - 8y = 40[/tex]
Subtract 12x from both sides
[tex]12x-12x - 8y = -12x+40[/tex]
[tex]- 8y = -12x+40[/tex]
Divide through by -8
[tex]\frac{- 8y}{-8} = \frac{-12x}{-8}+\frac{40}{-8}[/tex]
[tex]y= \frac{12x}{8}-\frac{40}{8}[/tex]
[tex]y= \frac{3}{2}x-5[/tex]
The slope intercept of an equation is: [tex]y = mx + b[/tex]
Where
[tex]m = slope[/tex]
By comparison:
[tex]m_4 = \frac{3}{2}[/tex]
So, the slopes of the lines are:
[tex]m_1 = -\frac{3}{2}[/tex] [tex]m_2 = -\frac{2}{3}[/tex] [tex]m_3 = -\frac{3}{2}[/tex] [tex]m_4 = \frac{3}{2}[/tex]
Lines with the same slope are parallel.
So:
Lines A and C with slope of [tex]-\frac{3}{2}[/tex] are parallel
Lines with the following relationship are perpendicular:
[tex]m * M = -1[/tex]
Lines B and D are perpendicular because:
[tex]-\frac{2}{3} * \frac{3}{2} = -1[/tex]
[tex]-\frac{6}{6} = -1[/tex]
[tex]-1 = -1[/tex]
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Answers
Answer:
200-300= -100
Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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Answers
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Answer:
Step-by-step explanation:
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Answers
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Answers
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Given:
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Answers
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Answers
Answer:
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Answers
Answer:
3
Step-by-step explanation:
x^5 = ?^5
x = 3
We plug in x = 3:
3^5 = ?^5
We find the fifth root of both sides and get:
3 = ?
That means that 3 is the answer
Answer:
3
Step-by-step explanation:
To evaluate the expression you would add in the x so in BLANK^3
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Answers
determine the solution to the equation.
Answers
5 x=32−7
5 x = 25
25x = 625
x=625/25
x=25
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Answers
Answer:
Texas had 34 electoral votes
Step-by-step explanation:
Ohio had 20 electoral votes in the recent presidential election.
Those 20 votes are 14 votes less than Texas had.
This means Texas had 14 votes more than Ohio, that is:
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Answers
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Answers
Answer:
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13. The first one
14. The last one
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Step-by-step explanation:
3)
Three angles are in the ratio 2:3:5
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Answers
Answer:
The other two angles are 75° and 125°.
Step-by-step explanation:
Let three angles are 2x, 3x and 5x.
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2x = 50
x = 25
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Answer:
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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Answer:
w= 3
Step-by-step explanation:
Add 7 to both sides of the equation w-7 = -4
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FIRST: In the space below, write an equation to represent the real-life situation. Remember, the variable and operation should be on one side of the equation and the total on the other.
SECOND: Solve the equation - make sure you show your work. Make sure you check your answer with a calculator and that your answer makes sense.plsss help ill give you 50 pointsss
Answers
Answer for Part A:
11 = 5 + 0.75g
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Answer for Part B:
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Answers
Answer:
The third and fifth are correct
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Answers
Answer:
Step-by-step explanation:
Your answer
Sale price = 144$
Mark it as Brainlist. Follow me for more answer.
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Answers
Answer:
-48
Step-by-step explanation:
the correct answer is,
[tex] - 48[/tex]
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Answers
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Answers
Answer:
y = 7x - 5
Step-by-step explanation:
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Here m = 7 and c = - 5, then
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Answers
Answer:
1, 18, 2, 9, 3, 6
I think
Answer:
Down Below!
Step-by-step explanation:
18 = 1 x 18, 2 x 9, or 3 x 6
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Answers
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Step-by-step explanation:
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Answers
Answer:
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Answers
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Answers
Answer:
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Step-by-step explanation:
Answer:
the equation will be y=-3x+4
Step-by-step explanation:
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Answers
Answer:
Step-by-step explanation:
Hey, I'm sorry I can't help but just know that it's going to be okay, school is also stressing me out. I'm so proud of you for staying alive. Have an amazing day :D
Answer:
21 3/8, 21 3/40, 21, -3/8,-21/40