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damaskus [11]
2 years ago
10

Harper is knitting a scarf for her cousin's birthday. She plans to knit every night, making the scarf 5 centimeters longer each

night. Write an equation that shows the relationship between the number of nights Harper spends knitting, x, and the length of the scarf in centimeters, y.
Mathematics
1 answer:
MissTica2 years ago
8 0

The equation that shows the relationship between x and y is:

y = 5x

A linear equation is in the form:

y = mx + b

where m is the rate of change and b is the initial value of y, y, x are variables.

Let x represent the number of nights knitting and y represent the length of the scarf.

The equation that shows the relationship between x and y is:

y = 5x

Find out more at: brainly.com/question/13911928

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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) (
aalyn [17]

we know that

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

in this problem we have

the point (5,12) is on the line of direct variation

so

Find the constant of proportionality k

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

the equation is

y=\frac{12}{5}x

Remember that

If a point is on the line of direct variation

then

the point must satisfy the equation of direct variation

we're proceeding to verify each point

<u>case A)</u> point (0,0)

x=0\ y=0

Substitute the value of x and y in the direct variation equation

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

0=0 -------> is true

therefore

the point (0,0) is on the line of direct variation

<u>case B)</u> point (2.5,6)

x=2.5\ y=6

Substitute the value of x and y in the direct variation equation

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

6=6 -------> is true

therefore

the point (2.5,6) is on the line of direct variation

<u>case C)</u> point (3,10)

x=3\ y=10

Substitute the value of x and y in the direct variation equation

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

10=7.2 -------> is not  true

therefore

the point (3,10) is not on the line of direct variation

<u>case D)</u> point (7.5,18)

x=7.5\ y=18

Substitute the value of x and y in the direct variation equation

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

18=18 -------> is true

therefore

the point (7.5,18) is on the line of direct variation

<u>case E)</u> point (12.5,24)

x=12.5\ y=24

Substitute the value of x and y in the direct variation equation

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

18=30 -------> is not true

therefore

the point  (12.5,24) is not on the line of direct variation

<u>case F)</u> point (15,36)

x=15\ y=36

Substitute the value of x and y in the direct variation equation

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

36=36 -------> is true

therefore

the point (15,36) is on the line of direct variation

therefore

<u>the answer is</u>

(0,0)

(2.5,6)

(7.5,18)

(15,36)


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