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BaLLatris [955]
3 years ago
8

A direct variation function contains the points (2, 14) and (4, 28). Which equation represents the function?

Mathematics
2 answers:
Svetlanka [38]3 years ago
5 0

we know that

A relationship between two variables, x, and y, represent a direct variation if it can be expressed in the form \frac{y}{x}=k or y=kx

In this problem we have

Points (2,14) and (4,28)

so

<u>Find the value of k</u>

First point

\frac{14}{2}=k

k=7

Second point

\frac{28}{4}=k

k=7

the function is

y=kx --------> substitute the value of k

y=7x

therefore

<u>the answer is</u>

y=7x

<u>In this problem with a single point was sufficient to calculate the equation, since in a direct variation the line passes through the origin, it is not necessary to use the formula of the slope</u>


Bogdan [553]3 years ago
3 0
A direct variation function, is just another way to word a "linear equation", and the slope will then be the "constant of variation".

so, in short, what's the equation of the line that runs through 2,14 and 4,28?

\bf \qquad \qquad \textit{direct proportional variation}\\\\&#10;\textit{\underline{y} varies directly with \underline{x}}\qquad \qquad  y=kx\impliedby &#10;\begin{array}{llll}&#10;k=constant\ of\\&#10;\qquad  variation&#10;\end{array}\\\\&#10;-------------------------------\\\\&#10;\begin{array}{lllll}&#10;&x_1&y_1&x_2&y_2\\&#10;%   (a,b)&#10;&({{ 2}}\quad ,&{{ 14}})\quad &#10;%   (c,d)&#10;&({{ 4}}\quad ,&{{ 28}})&#10;\end{array}

\bf slope = {{ m}}= \cfrac{rise}{run} \implies &#10;\cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{28-14}{4-2}\implies \cfrac{14}{2}\implies 7&#10;\\\\\\&#10;% point-slope intercept&#10;\stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-14=7(x-2)&#10;\\\\\\&#10;y-14=7x-14\implies y=7x
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