Question

1) If y varies inversely as x, and y=3 as x = -2, find y for the x value of -1.
2) If y varies directly as x, and y=15 as x=-3, find y for the x value of 4

Answer 1

Answer:

Part 1) y=6

Part 2) y=-20

Step-by-step explanation:

Part 1) If y varies inversely as x, and y=3 as x = -2, find y for the x value of -1.

we know that

A relationship between two variables, x, and y, represent an inverse variation if it can be expressed in the form $y*x=k$ or $y=k/x$

we have

For x=-2, y=3

Find the value of the constant k

$k=y*x$

substitute the values of x and y

$k=(3)(-2)=-6$

The equation is equal to

$y=-6/x$

so

For x=-1

substitute in the equation and solve for y

$y=-6/(-1)=6$

Part 2) If y varies directly as x, and y=15 as x=-3, find y for the x value of 4

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 $y=kx$

we have

For x=-3, y=15

Find the value of the constant k

$k=y/x$

substitute the values of x and y

$k=15/-3=-5$

The equation is equal to

$y=-5x$

so

For x=4

substitute in the equation and solve for y

$y=-5(4)=-20$