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3 months ago

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What other points are on the line of direct variation through (5, 12)? Check all that apply. (0, 0) (2.5, 6) (3, 10) (7.5, 18) (

12.5, 24) (15, 36)

2 answers:

Leona [12.6K]3 months ago

6 0

Here are the solutions along with the graph

Inessa [12.5K]3 months ago

5 0

It is established that

A correlation between two variables, x and y, demonstrates a direct variation if it can be written in the format $y/x=k$ or $y=kx$

For this question, we have

the point $(5,12)$ lies on the direct variation line

therefore

Determine the constant of proportionality k

$y/x=k$ -------> substitute ------> $k=12/5$

The equation is

$y=\frac{12}{5}x$

Keep in mind that

If a point is located on the direct variation line

then

the point has to fulfill the direct variation equation

we will now validate each point

case A) point $(0,0)$

$x=0\ y=0$

Insert the values of x and y into the direct variation equation

$0=\frac{12}{5}*0$

$0=0$ -------> is valid

thus

the point $(0,0)$ lies on the direct variation line

case B) point $(2.5,6)$

$x=2.5\ y=6$

Insert the values of x and y into the direct variation equation

$6=\frac{12}{5}*2.5$

$6=6$ -------> is valid

thus

the point $(2.5,6)$ lies on the direct variation line

case C) point $(3,10)$

$x=3\ y=10$

Insert the values of x and y into the direct variation equation

$10=\frac{12}{5}*3$

$10=7.2$ -------> is not valid

thus

the point $(3,10)$ does not lie on the direct variation line

case D) point $(7.5,18)$

$x=7.5\ y=18$

Insert the values of x and y into the direct variation equation

$18=\frac{12}{5}*7.5$

$18=18$ -------> is valid

thus

the point $(7.5,18)$ lies on the direct variation line

case E) point $(12.5,24)$

$x=12.5\ y=24$

Insert the values of x and y into the direct variation equation

$24=\frac{12}{5}*12.5$

$18=30$ -------> is not valid

thus

the point $(12.5,24)$ does not lie on the direct variation line

case F) point $(15,36)$

$x=15\ y=36$

Insert the values of x and y into the direct variation equation

$36=\frac{12}{5}*15$

$36=36$ -------> is valid

thus

the point $(15,36)$ lies on the direct variation line

ultimately

the solution is

$(0,0)$

$(2.5,6)$

$(7.5,18)$

$(15,36)$

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