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lara31 [8.8K]
3 years ago
14

Use slopes and y-intercepts to determine if the lines y=5x+5 and 5x−y=−5 are parallel.

Mathematics
1 answer:
GalinKa [24]3 years ago
7 0

Answer: They are not parallel, they are coincident

Step-by-step explanation:

If two lines have the same slope but a different y-intercept, the lines are parallel. If two lines have the same slope and the same y-intercept, the lines are coincident.

We can rewrite 5x−y=−5 adding -5x to both sides and multiplying by -1:

5x - y =-5

5x - y -5x = -5 - 5x (adding -5x to both sides)

-y = -5 - 5x

Multiplying by -1

y = 5x + 5

Both equations look the same so they are coincident. They have the same intercept y=5 and the same slope m=5.

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A. {0,1,2,3,4}<br> B. {1,2,3,4}<br> C. {-1,0,1,2,3}<br> D. {-2,-1,0,1,2,3,4}
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The set is {-2, -1, 0, 1, 2, 3, 4}.

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\{x \in Z:-2 \leq x \leq 4\}

Z means integer values.

Integer means set of positive and negative values including zero.

-2 \leq x \leq 4

This means x lies between -2 and 4.

  • If x strictly less than -2 and greater than 4 means you don't have to include -2 and 4.
  • But here x less than or equal to -2 and greater than or equal to 4, so you have to include -2 and 4.

The integers are -2, -1, 0, 1, 2, 3 and 4.

So, x belongs to the set {-2, -1, 0, 1, 2, 3, 4}

Hence the given set is defined by the set  {-2, -1, 0, 1, 2, 3, 4}.

Option D is the correct answer.

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