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$$-\frac{3}{6}=k$$-\frac{1}{2}=k$

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

$y=-\frac{1}{2}x$

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=\frac{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=\frac{y2-y1}{x2-x1}$$m=\frac{8-3}{3-4}$$m=\frac{5}{-1}$$m=-5$

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

m=5