Determine whether y varies directly with x. Find the constant of variation. Write the function rule x 5 7 9 y 6 11 16

Mathematics

1 answer:

daser333 [38]4 years ago

4 0

Answer:

a) y does NOT vary directly with x

b) y = 2.5x -6.5

Step-by-step explanation:

If variation were direct the ratios of y to x would be constant. They are not:

6/5 ≠ 11/7

y does not vary directly with x.

y changes by 5 from 6 to 11 when x changes by 2 from 5 to 7. Then the slope of the linear function rule is (change in y)/(change in x) = 5/2. Using a point-slope form of the equation of a line, we can write the rule as ...

y = m(x -h) +k . . . . . . . . for a line of slope m through point (h, k)

y = (5/2)(x -5) +6

y = 2.5x -6.5 . . . . . simplify

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dem82 [27]

Answer:

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Step-by-step explanation:

Rationalizing the denominator of a fraction is when one multiplying fraction such that it removes any radical from the denominator. This can be done by multiplying both the numerator and the denominator by the radical that is present in the denominator. In fractional terms, a number over itself is equal to one, therefore, doing this would keep the equation true. After multiplying, one will simplify the resulting fraction.

$\frac{17}{4\sqrt{17}} * \frac{\sqrt{17}}{\sqrt{17}}\\\\= \frac{17\sqrt{17}}{4(17)}\\$