What is the equation, in slope-intercept form, of the line that contains the points (3, -4) and (5 -6)

Mathematics

1 answer:

Alika [10]3 years ago

4 0

Answer:

y = -x - 7

Step-by-step explanation:

As we move from the point (3, -4) to the point (5, -6), x increases by 2 and y decreases by 2. Thus, the slope of this line is m = rise / run = -2/2, or -1.

Starting with the general slope-intercept form of the equation of a straight line, we get y = mx + b => y = -1x + b.

Subbing -4 for y and 3 for x, we get

-4 = -1(3) + b, which yields b = -1

Thus, the desired equation is

y = -x - 1

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Ryan has $3$ red lava lamps and $3$ blue lava lamps. He arranges them in a row on a shelf randomly, then turns $3$ random lamps

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There are 6! = 720 ways of arranging the lamps.

If the leftmost lamp is red, there are 3 choices of lamp in the leftmost position, and the remaining 5 can be placed in any order, so there are 3×5! = 360 ways of arranging the lamps and the leftmost is red.

Hence there is a 360/720 = 1/2 probability that the leftmost lamp is red.

Ignoring lamp color for the moment, the probability of arranging 3 lit lamps and 3 unlit lamps is the same, 1/2.

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2 years ago

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ahrayia [7]

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