All categories

3 years ago

Which relation is a direct variation that contains the ordered pair (2, 7)?

Mathematics

1 answer:

Vedmedyk [2.9K]3 years ago

5 0

Answer:

$y=\frac{7}{2}x$

Step-by-step explanation:

we know that

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

In a direct relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

step 1

Find the value of the constant of proportionality k

we have

the ordered pair (2, 7)

$k=\frac{y}{x}$ -----> $k=\frac{7}{2}$

therefore

The relation is

$y=kx$ -----> $y=\frac{7}{2}x$

You might be interested in

How deep is the water 31.5 feet from the shore? 05 (10 Points)

pantera1 [17]

Answer:

This is impossible to answer, unless there is a picture that is not there.

Step-by-step explanation:

6 0

2 years ago

3.201 in expanded form

Gnoma [55]

Heya!

Here is your answe:

3.201= 3+ 0.200+ 0.001

:)

8 0

3 years ago

Read 2 more answers

The following pattern starts with 4 and uses the rule add 6 to the previous term.

Harrizon [31]

Answer:

Every number in the pattern is greater than the previous number.

6 0

3 years ago

Which equation does the graph of the systems of equations solve?

mihalych1998 [28]

Answer:

$\text{B. }\frac{1}{3}x-3=-x+1$

Step-by-step explanation:

Let's start by taking a look at the blue line. The slope of any line that passes through two points is equal to the change in y-values over the change in x-values. We can see that the line passes through points (0, 1) and (1, 0). Assign these points to $(x_1,y_1)$ and $(x_2, y_2)$ (doesn't matter which you assign) and use the slope formula:

$m=\frac{y_2-y_1}{x_2-x_1}$

Let:

$(x_1,y_1)\implies (0,1)\\(x_2,y_2)\implies (1, 0)$

The slope is equal to:

$m=\frac{0-1}{1-0}=\frac{-1}{1}=-1$

Therefore, the slope of this line is -1. In slope-intercept form $y=mx+b$ , $m$ represents slope, so one of the lines must have a term with $-x$ in it, which eliminates answer choices A and D.

For the second line, do the same thing. The red line clearly passes through (0, -3) and (3, -2). Therefore, let:

$(x_1,y_1)\implies (0,-3)\\(x_2,y_2)\implies (3, -2)$

Using the slope formula:

$m=\frac{-2-(-3)}{3-0}=\frac{1}{3}$

Thus, the slope of the line is 1/3 and the other line must have a term with $\frac{1}{3}x$ in it, eliminating answer choice C and leaving the answer $\boxed{\text{B. }\frac{1}{3}x-3=-x+1}$

*You can find the exact equation of each line by using the slope formula as shown and plugging in any point the line passes through into $y=mx+b$

7 0

3 years ago

Who’s graph show a proportional relationship in which the value of y is one-half of the value of x

Sunny_sXe [5.5K]

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form y/x=k or y=kx

That means it's the equation of a line passing through the origin.

case a) and case d) are discarded because the line does not pass through the origin

case b) we have

for x=2 y=4

y/x=k-------> 4/2=2------> k=2

y=2x-------> in this case the value of y is two times the value of x

case c) we have

for x=4 y=2

y/x=k-------> 2/4=1/2------> k=(1/2)

y=(1/2)x-------> in this case the value of y is one-half of the value of x

therefore

the solution is the case c) see the attached figure

8 0

3 years ago