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4 years ago

13

A direct variation function contains the points (2,14) and (4,38) which equation represents the function

1 answer:

Dmitry [639]4 years ago

3 0

You are given two points on a line, and told that the function is "direct variation." You can save a lot of time by recognizing that the y-intercept here is zero (0). Thus, the line passes through the origin.

A line through (2,14) and (4,38) is NOT direct variation, because the line connecting those two points does NOT pass through the origin, and thus has a vertical intercept.

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Romashka [77]

Answer:

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Step-by-step explanation:

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4 0

3 years ago

NEED HELP ASAP PLEASE!!

qwelly [4]

Option D:

$$y=\frac{5x-2}{x}$

Solution:

Given function:

$$y=\frac{-2}{x-5}$

To find the inverse of the function.

<u>Inverse of a function:</u>

<em>If a function f(x) is mapping x to y, then the inverse function of f(x) maps y back to x.</em>

$$y=\frac{-2}{x-5}$

Interchange the variables x and y.

$$x=\frac{-2}{y-5}$

Now, solve for y.

Multiply both sides by (y - 5).

$$x(y-5)=-\frac{2}{y-5}(y-5)$

Cancel the common factors, we get

$x(y-5)=-2$

Divide by x on both sides.

$$y-5=-\frac{2}{x}$

Add 5 on both sides.

$$y=-\frac{2}{x}+5$

$$y=-\frac{2}{x}+\frac{5}{1}$

To make the denominator same, multiply the 2nd term by $\frac{x}{x}$ .

$$y=-\frac{2}{x}+\frac{5x}{x}$

$$y=\frac{-2+5x}{x}$

$$y=\frac{5x-2}{x}$

Option D is the correct answer.

8 0

3 years ago