91Ó°ÊÓ

For each set of equations, tell what the graphs of all four relationships have in common without drawing the graphs. Explain your answers. $$\begin{array}{l}{y=2 x} \\ {y=-2 x} \\ {y=3 x} \\ {y=-3 x}\end{array}$$

In this exercise, you will apply what you have learned about writing equations for parallel lines. a. Write three equations whose graphs are parallel lines with positive slopes. Write the equations so that the graphs are equally spaced. b. Graph the lines, and verify that they are parallel. c. Write three equations whose graphs are parallel lines with negative slopes and are equally spaced. d. Graph the lines, and verify that they are parallel.

Three cellular telephone companies have different fee plans for local calls. i. Talk-It-Up offers a flat rate of \(\$ 50\) per month. You can talk as much as you want for no extra charge. i. One Thin Dime charges \(\$ 0.10\) for each half minute, with no flat rate. iii. CellBell charges \(\$ 30\) per month and then \(\$ 0.10\) per minute for all calls made. a. For each company, write an equation that relates the cost of the phone service, \(c\), to the number of minutes a customer talks during a month, \(t\). b. Any linear equation can be written in the form \(y=m x+b\) . Give the value of \(m\) and \(b\) for each equation you wrote in Part a. c. For each company, make a graph that relates the cost of the phone service to the number of minutes a customer talks during a month. d. Where do the values of \(m\) and \(b\) appear in the graph for each phone company?

Use the distributive property to rewrite each expression without using parentheses. 2\(a\left(0.5 z+z^{2}\right)\)

For Exercises 20–28, answer Parts a and b. a. What is the constant difference between the \(y\) values as the \(x\) values increase by 1\(?\) b. What is the constant difference between the \(y\) values as the \(x\) values decrease by 2\(?\) $$y=x$$

For Exercises 20–28, answer Parts a and b. a. What is the constant difference between the \(y\) values as the \(x\) values increase by 1\(?\) b. What is the constant difference between the \(y\) values as the \(x\) values decrease by 2\(?\) $$ y=3 x-3 $$

The table shows x and y values for a particular relationship. $$\begin{array}{|c|c|c|c|c|}\hline x & {6} & {3} & {1} & {2.5} \\ \hline y & {7} & {1} & {-3} & {0} \\ \hline\end{array}$$ $$\begin{array}{l}{\text { a. Graph the ordered pairs }(x, y) . \text { Make each axis scale from }-10} \\ {\text { to } 10 .} \\ {\text { b. Could the points represent a linear relationship? If so, write an }} \\ {\text { equation for the line. }} \\ {\text { c. From your graph, predict the } y \text { value for an } x \text { value of }-2 . \text { Check }} \\ {\text { your answer by substituting it into the equation. }}\end{array}$$ $$ \begin{array}{l}{\text { d. From your graph, find the } x \text { value for a } y \text { value of }-2 . \text { Check your }} \\ {\text { answer by substituting it into the equation. }} \\ {\text { e. Use your equation to find the } y \text { value for each of these } x \text { values: }} \\ {0,-- 1,-1.5,-2.5 . \text { Check that the corresponding points all lie on }} \\\ {\text { the line. }}\end{array} $$