Chapter 2

Make a table of values for each equation. Then graph the equation. $$ y=|4 x| $$

Graph each inequality. $$ y>2 x+1 $$

For each function, graph the function by translating the parent function. \(y=|x|-3\)

A car enters an interstate highway 15 \(\mathrm{mi}\) north of a city. The car travels due north at an average speed of 62.5 milh. Write an equation to model the car's distance \(d\) from the city after traveling for \(h\) hours. Graph the equation.

For each function, determine whether \(y\) varies directly with \(x\) . If so, find the constant of variation and write the equation. \(\begin{array}{|c|c|}\hline x & {y} \\ \hline 2 & {4} \\ {4} & {8} \\ {16} & {32} \\ \hline\end{array}\)

Graph each equation. Check your work. $$ y=2 x $$

Graph each relation. $$ \\{(-1,3),(-2,1),(-3,-3),(-4,-5)\\} $$

Make a table of values for each equation. Then graph the equation. $$ y=|4 x|-1 $$

Graph each inequality. $$ y<3 $$

For each function, graph the function by translating the parent function. \(y=|x|+4 \frac{1}{2}\)

A pump removes 1000 gal of water from a pool at a constant rate of 50 gal/min. a. Write an equation to find the amount of water \(y\) in the pool after \(t\) minutes. b. Graph the equation and interpret the \(t\) - and \(y\) -intercepts.

For each function, determine whether \(y\) varies directly with \(x\) . If so, find the constant of variation and write the equation. \(\begin{array}{|c|c|}\hline x & {y} \\ \hline 2 & {-6} \\ {4} & {-12} \\\ {5} & {-15} \\ \hline\end{array}\)

Graph each equation. Check your work. $$ y=-3 x-1 $$

Graph each relation. $$ \\{(0,-2),(2,0),(3,1),(5,3)\\} $$

Make a table of values for each equation. Then graph the equation. $$ y=|4 x-1| $$

Graph each inequality. $$ x \leq 0 $$

For each function, graph the function by translating the parent function. \(y=|x|+2\)

A tree 5 ft tall grows an average of 8 in. each year. Write and graph an equation to model the tree's height \(h\) after \(x\) years.

Graph each equation. Check your work. $$ y=3 x-2 $$

Graph each relation. $$ \left\\{(-1,0),\left(\frac{1}{2},-1\right),\left(0, \frac{1}{2}\right),\left(-1,-\frac{1}{2}\right)\right\\} $$

Make a table of values for each equation. Then graph the equation. $$ y=|-3 x| $$

Graph each inequality. $$ y \leq x-5 $$

For each function, graph the function by translating the parent function. \(y=|x|-6\)

For each situation, find a linear model and use it to make a prediction. There are 2 leaves along 3 in. of an ivy vine. There are 14 leaves along 15 in. of the same vine. How many leaves are there along 6 in. of the vine?

For each function, determine whether \(y\) varies directly with \(x\) . If so, find the constant of variation and write the equation. \(\begin{array}{|c|c|}\hline x & {y} \\ \hline 27 & {9} \\ \hline 30 & {10} \\\ {60} & {20} \\ \hline\end{array}\)

Graph each equation. Check your work. $$ y=-4 x+5 $$

Graph each relation. $$ \left\\{\left(2 \frac{1}{2}, 0\right),\left(-\frac{1}{2}, 0\right),(2,0),(0,0)\right\\} $$

Make a table of values for each equation. Then graph the equation. $$ y=|-3 x|+2 $$

Graph each inequality. $$ 2 x+3 y \geq 12 $$

For each situation, find a linear model and use it to make a prediction. An empty 5 -gal water jug weighs 0.75 lb. With 3 \(\mathrm{c}\) of water inside, the jug weighs 2.25 lb. Predict the weight of the jug with 5 \(\mathrm{c}\) of water inside.

For each function, determine whether \(y\) varies directly with \(x\) . If so, find the constant of variation and write the equation. \(\begin{array}{|c|c|}\hline x & {y} \\ \hline 2 & {14} \\ {3} & {21} \\ {5} & {35} \\ \hline\end{array}\)

Graph each equation. Check your work. $$ 5 x-2 y=-4 $$

Make a table of values for each equation. Then graph the equation. $$ y=|-3 x+2| $$

Graph each inequality. $$ 2 y \geq 4 x-6 $$

Write an equation for each vertical translation of \(y=|x|\). 4 units up

For each situation, find a linear model and use it to make a prediction. There are 55 blades of grass in 1 in. 2 of lawn. There are 230 blades of grass in 4 in. 2 of the same lawn. How many blades of grass are in 3 in. 2 of lawn?

Graph each equation. Check your work. $$ -2 x+5 y=-10 $$

Make a table of values for each equation. Then graph the equation. $$ y=-|2 x| $$

Graph each inequality. $$ y>\frac{2}{3} x+\frac{1}{3} $$

Write an equation for each vertical translation of \(y=|x|\). 2 units up

For each situation, find a linear model and use it to make a prediction. A 2 -mi cab ride costs \(\$ 5.25 .\) A 5 -mi cab ride costs \(\$ 10.50 .\) How much does a 3.8 -mi cab ride cost?

For each function, determine whether \(y\) varies directly with \(x\) . If so, find the constant of variation and write the equation. \(\begin{array}{|c|c|}\hline x & {y} \\ \hline-2 & {4} \\ {-3} & {6} \\ {-5} & {10} \\ \hline\end{array}\)

Graph each equation. Check your work. $$ y-3=-2 x $$

Graph each inequality. $$ 3 x-2 y \leq 9 $$

Make a table of values for each equation. Then graph the equation. $$ y=-|2 x|+5 $$

For each function, identify the translation of the parent function. Then graph the function. \(y=|x-4|\)

Graph each set of data. Decide whether a linear model is reasonable. If so, draw a trend line and write its equation. $$ \\{(0,11),(2,8),(3,7),(7,2),(8,0)\\} $$

Graph each equation. Check your work. $$ y+4=-3 x $$

Make a mapping diagram for each relation. $$ \\{(0,0),(-1,-1),(-2,-8),(-3,-27)\\} $$

Graph each inequality. $$ 5 x>-y+3 $$