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mel-nik [20]
3 years ago
9

Are the graphs of the lines in the pair parallel? Explain. y = 6x + 9 27x – 3y = –81 No, since the y-intercepts are different. Y

es, since the slopes are the same and the y-intercepts are different. No, since the slopes are different. Yes, since the slopes are the same and the y-intercepts are the same.
Mathematics
1 answer:
Dominik [7]3 years ago
4 0

Answer:

No, since the slopes are different

Step-by-step explanation:

Parallel lines by definition have the same slope but different y-intercepts. The slope of the line  y = 6x + 9 is 6, the coefficient of x since the equation is given in slope-intercept form. Its y-intercept is 9.

For the second equation, 27x – 3y = –81 , we have to solve for y or re-write the equation in slope-intercept form;

-3y = -27x - 81

y = 9x + 27

The slope of this line is thus 9, the coefficient of x since the equation is in slope-intercept form. Its y-intercept is 27.

The two equations have different slopes and thus they are not parallel

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Triangle ABC is translated to create triangle DFG, as shown below.
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Answer:

x=3

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Step-by-step explanation:

Given

The translated triangles

Required

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We have:

AB = DF

BC = FG

AB = DF means:

3(2x + 10) = 12x + 12

Open bracket

6x + 30 = 12x + 12

Collect like terms

12x - 6x = 30 -12

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Divide by 6

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BC = FG means

2y + 12 = 2(2y - 3)

Open bracket

2y + 12 = 4y - 6

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3 years ago
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Julli [10]

Answer:

→ The table is:

→  x  →  -1   →  0  →  1

→  y  →  -3  →  0  →  3

The graph of the line is figure d

Step-by-step explanation:

∵ y = 3x

∵ x = -1, 0, 1

→ Substitute the values of x in the equation to find the values of y

∴ y = 3(-1) = -3

∴ y = 3(0) = 0

∴ y = 3(1) = 3

→ The table is:

→  x  →  -1   →  0  →  1

→  y  →  -3  →  0  →  3

∵ The form of the linear equation is y = m x + b, where

  • m is the slope
  • b is the y-intercept

∵ y = 3x

→ Compare the equation with the form

∴ m = 3

∴ b = 0

→ That means the slope is positive, then the direction of the line must

   be from left tp right and passes through the origin

∴ The graph of the line is figure d

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Step-by-step explanation:

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