Question

1)What is the correct equation for direct variation that includes the point (6, –3)?2)The product of two positive integers is 72. The first is 6 less than the second.Find the integers.3)The price of turkey depends on its weight. Suppose turkeys sell for $0.59 perpound. What is the price of a 10–pound turkey?4)Find the slope of the line that passes through the points (4, 3), (3, 8).5)

Answer 1

1.What is the correct equation for direct variation that includes the point (6, –3)?

a direct variation is given by the expression

`y=kx`

since the variation includes the points (6 , -3) let's assume

x=6

y=-3

then

`-3=6k`
`-(3)/(6)=k`
`-(1)/(2)=k`

the the expression for direct variation that includes the point (6, –3) is

`y=-(1)/(2)x`

2.The product of two positive integers is 72. The first is 6 less than the second.

Find the integers.

from the expression

product of two positive integers is 72

`a*b=72`

and from the expression

The first is 6 less than the second.

`a-6=b`

then let's solve a and b

since b= a-6

then

`a*(a-6)=72`
`a^2-6a=72`
`a=12,a=-6`

then

`a-6=b`
`12-6=6`

and

`-6-6=-12`

then the posible answers are

a=12, b=6

a=-6, b=-12

since The product of two positive integers the only possible answer is

a=12, b=6

3.The price of turkey depends on its weight. Suppose turkeys sell for $0.59 per

pound. What is the price of a 10 pound turkey?

0.59 = 1 pound

x= 10 pounds

then

`x=(10pounds)/(1pound)*0.59`
`x=5.9`

then 10 pounds cost $5.9

4)4)Find the slope of the line that passes through the points (4, 3), (3, 8).

the slope is given by

`m=(y2-y1)/(x2-x1)`
`m=(8-3)/(3-4)`
`m=(5)/(-1)`
`m=-5`

then the slope of the line that passes through the points (4, 3), (3, 8). is

m=5