91Ó°ÊÓ

Express each combined variation as an equation. Then find the requested value. Assume that all variables represent positive numbers. SEE EXAMPLE 4. (OBJECTIVE 4) \(y\) varies directly with the square of \(x\) and inversely with \(z\). If \(y=1\) when \(x=2\) and \(z=10\), find \(y\) when \(x=4\) and \(z=5\).

Graph each function and state the domain and range. $$y=\frac{1}{2} x-3$$

Explain how to plot the point with coordinates (-2,5).

Set up a variation equation and solve for the requested value. The force of gravity acting on an object varies directly with the mass of the object. The force on a mass of 5 kilograms is 49 newtons. What is the force acting on a mass of 12 kilograms?

Set up a variation equation and solve for the requested value. For a fixed area, the length of a rectangle is inversely proportional to its width. A rectangle has a width of 8 feet and a length of 10 feet. If the length is increased to 16 feet, find the width of the rectangle.

Graph each equation using any method. $$y=4.5 x+2$$

Three years after a cottage was purchased it was appraised at \(147,700\)dollar. The property is now 10 years old and is worth \(172,200\)dollar. Find its original purchase price.

Explain the meaning of combined variation.

Find the slopes of lines \(P Q\) and \(P R\) and determine whether the points \(P, Q,\) and \(R\) lie on the same line. (Hint: Two lines with the same slope and a point in common must be the same line.) $$P(-2,4), Q(4,8), R(8,12)$$

Find the slopes of lines \(P Q\) and \(P R\) and determine whether the points \(P, Q,\) and \(R\) lie on the same line. (Hint: Two lines with the same slope and a point in common must be the same line.) $$P(6,10), Q(0,6), R(3,8)$$