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3 years ago

Prove that Two lines are parallel if and only if they have the same slope

Mathematics

1 answer:

Gennadij [26K]3 years ago

8 0

Given line q and line r, with equations

y = m x + b1 y = m x + b2

such that these are different lines, with identical slopes. Prove that line q || line r.

If these lines are parallel, then they will not intersect. Assume the lines intersect. Calculate the point of intersection. Since these equations already have the same slope, we may as well subtract one equation from the other one.

This gives us the following equation:

0 = b1 - b2 b1 = b2

If b1 = b2, then line q is the same line as line r. This contradicts the given conditions.

Therefore, line q and line r cannot intersect. If line q and line r do not intersect, they must be parallel.

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2 years ago

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When you add two rational numbers, each number can be written as a?

ra1l [238]

The correct answer to your question is... a rational #, because when you add two rational #'s, each # can be written as a rational #.

Reasoning:
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By the way # means number.

I hope this helps!
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3 years ago

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2 years ago

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Evaluate the integral. (3 + 1/4 u^4 − 2/3 u^9) du

polet [3.4K]

(3 + 1/4 u^4 − 2/3 u^9) du

6 0

2 years ago

Someone help me asap pls

Makovka662 [10]

Answer:

For the graph in the top-left corner, the ?? = 0.25

This can be found using a simple slope equation:

m = (y2-y1)/(x2-x1)

m = slope

You take two coordinates, in this case (8, 2) and (4, 1), label one as #1 and the other as #2, and plug in the values so:

slope = (2-1)/(8-4)

slope = 1/4 or 0.25

The equation of a line is y = mx + b and if you were to place 0.25, or 1/4, in place of m (the slope) and 1 in the place of x since it is the x value, and multiply, you would end up with 0.25.

This also gives you the answer to your next two questions.

The one in the top-right corner is $0.25 per pencil.

The answer to the question just below it is y = 0.25x.

b in the equation would equal 0 since b is the y-intercept (where the line crosses the y-axis)

As for the last one, you simply have to multiply 30 by each number in the left column since you already know 30 miles are travelled in 1 hour, giving you your rate or the equation of the line, y=x.

The missing values of the table are as follows:

0, 60, 150, 240, 330, 1470

Finally, the last box:

Miles = 30 * hours

y = 30x

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3 years ago