Mathematics, 30.07.2019 02:00 alexdonatalex1314

For the data in the table, does y vary directly with x? if it does, write an equation for the direct variation. x = -6 , 1 , 8 y = 9 , -1.5 , -12

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X = -6 y = 9
x = 1 y = -1.5
x = 8 y = -12

the statement "y varies directly with x" means that when x increases, y increases by the same factor. in other words, y and z always have the same ratio.

$\frac{y}{x}$ = k

where k is the constant variation. the relationship between x and y can also be expressed as: y = kx

since k is constant (the same for every point), we can find k when given any point by dividing the y-coordinate by the x-coordinate. for example, if y varies directly as x, and y = 6 when x = 2, the constant of variation is k = $\frac{6}{2}$ = 3. therefore, the equation describing this direct variation is y = 3x.

k = $\frac{9}{-6}$ simplify it
y = $\frac{-3}{2}$ x

k = $\frac{-1.5}{1}$
y = -1.5x

k = $\frac{-12}{8}$
y = $-\frac{3}{2}$ x

Answer from: Quest

answer: b i think

step-by-step explanation:

Answer from: Quest

step-by-step explanation:

30% of $420 is 0.30($420) = $126 and $420 + $126 = $546.

or, 130% of $420 is 1.3($420) = $546.

notice that this is not the $600 original list price with which we started.

why doesn't this work?

the method does not work because 30% of $420 is not the same amount as the 30% of $600. it may seem obvious when stated this way, but it is a very common error made on problems of this type. we cannot just use the same percent and get back to the original amount because we are taking that percent of a different value.

to work problems of this type correctly, it is generally best to write an equation for the situation and then solve.

example: since (100% – 30%)(original price) = (sale price)

70% of the (original price) is $420.

0.7x = 420

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x = 600

the original cost was $600.

we may also solve this problem using the two-step method. working the problem in two steps requires us to use more algebra skills. we have to know that x = 1x (identity property of multiplicationtext annotation indicator) and that 1x – 0.3x = 0.7x (subtracting like terms). then we solve the problem as follows:

(original price) – 30%(original price) = sale price

x – 0.3x = 420

0.7x = $420

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x = 600

the original cost was $600.

note that with both of the above methods we do obtain the correct original amount.

example: after a 5% pay raise, hermione is earning $22,680 per year. what was she earning before the pay raise?

105% of (original salary) = current salary

1.05x = 22,680

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x = 21,600