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3 years ago

Assume that y varies inversely with x. If y = -6 when x = -2, find y when x = 5.

Mathematics

1 answer:

77julia77 [94]3 years ago

7 0

Answer:

y = 2.4

Step-by-step explanation:

If y varies inversely as x, it means there's an inverse relationship between y and x, that is if x is increasing, y is decreasing and vice versa. In such instance, we have to find the constant of proportionality "k"

Hence,

y~1/x

y=k/x

When y =-6 and x =-2, we insert these values to find the value of the constant "k"

-6 = k/-2

k = 12.

Using this value of k to determine value of y when x =5 becomes:

y = 12/5

y = 2.4

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Solve the system of equations - 6x + 5y = 0 and -5x + 5y = -5 by combining

Anna [14]

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Answer:

(x, y) = (-5, -6)

Step-by-step explanation:

The coefficients of y are the same, so we can eliminate y by subtracting one equation from the other. Here, we choose to subtract the first from the second, so that the coefficient of x ends up positive.

(-5x +5y) -(-6x +5y) = (-5) -(0)

x = -5 . . . . . . simplify

-6(-5) +5y = 0 . . . . . . substitute x into the first equation

6 +y = 0 . . . . . . . . . . divide by 5

y = -6 . . . . . . subtract 6

The solution to the system of equations is (x, y) = (-5, -6).

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2 years ago

A line includes the points (4,1) and (8, 2). What is its equation in slope-intercept form?

Alisiya [41]

Answer:

$y = \frac{1}{4} x$

Step-by-step explanation:

1) First, find the slope of the equation. Use the slope formula $m= \frac{y_2-y_1}{x_2-x_1}$ . Substitute the x and y values of the given points into the formula and solve:

$m = \frac{(2)-(1)}{(8)-(4)} \\m = \frac{2-1}{8-4}\\m = \frac{1}{4}$

Thus, the slope is $\frac{1}{4}$ .

2) Now, use the point-slope formula $y-y_1 = m (x-x_1)$ to write the equation in point-slope form (from there we can convert it to slope-intercept). Substitute values for $m$ , $x_1$ , and $y_1$ .

Since $m$ represents the slope, substitute $\frac{1}{4}$ for it. Since $x_1$ and $y_1$ represent the x and y values of one point the line intersects, choose any of the given points (it doesn't matter which one, the end result will be the same) and substitute its x and y values into the formula as well. (I chose (4,1), as seen below.) Then, isolate y to put the equation in slope-intercept form and find the answer.

$y-(1) = \frac{1}{4} (x-4)\\y-1 = \frac{1}{4} x-1\\y = \frac{1}{4} x+0\\y=\frac{1}{4}x$

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2 years ago