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4.9: Chapter 4 Review

Difficulty Level: At Grade Created by: CK-12

Define the following words:

1. x\begin{align*}x-\end{align*}intercept
2. y\begin{align*}y-\end{align*}intercept
3. direct variation
4. parallel lines
5. rate of change

In 6 – 11, identify the coordinates using the graph below.

1. D\begin{align*}D\end{align*}
2. F\begin{align*}F\end{align*}
3. A\begin{align*}A\end{align*}
4. E\begin{align*}E\end{align*}
5. B\begin{align*}B\end{align*}
6. C\begin{align*}C\end{align*}

In 12 – 16, graph the following ordered pairs on one Cartesian Plane.

1. (12,4)\begin{align*}\left (\frac{1}{2},-4\right )\end{align*}
2. (–6, 1)
3. (0, –5)
4. (8, 0)
5. (32,84)\begin{align*}\left (\frac{3}{2},\frac{8}{4}\right )\end{align*}

In 17 and 18, graph the function using the table.

x\begin{align*}x\end{align*} y\begin{align*}y\end{align*}
–2 7
–1 9
0 11
1 13
2 15
1. dt0017521503225430053756450\begin{align*}& d && 0 && 1 && 2 && 3 && 4 && 5 && 6\\ & t && 0 && 75 && 150 && 225 && 300 && 375 && 450\end{align*}

In 19 – 24, graph the following lines on one set of axes.

1. y=32\begin{align*}y=-\frac{3}{2}\end{align*}
2. x=4\begin{align*}x=4\end{align*}
3. y=5\begin{align*}y=5\end{align*}
4. x=3\begin{align*}x=-3\end{align*}
5. x=0\begin{align*}x=0\end{align*}
6. y=0\begin{align*}y=0\end{align*}

In 25 – 28, find the intercepts of each equation.

1. y=4x5\begin{align*}y=4x-5\end{align*}
2. 5x+5y=20\begin{align*}5x+5y=20\end{align*}
3. x+y=7\begin{align*}x+y=7\end{align*}
4. 8y16x=48\begin{align*}8y-16x=48\end{align*}

In 29 – 34, graph each equation using its intercepts.

1. 3x+7y=21\begin{align*}3x+7y=21\end{align*}
2. 2y5x=10\begin{align*}2y-5x=10\end{align*}
3. xy=4\begin{align*}x-y=4\end{align*}
4. 16x+8y=16\begin{align*}16x+8y=16\end{align*}
5. x+9y=18\begin{align*}x+9y=18\end{align*}
6. 7+y=17x\begin{align*}7+y=\frac{1}{7} x\end{align*}

In 35 – 44, find the slope between the sets of points.

1. (3, 20) and (19, 8)
2. (12, 5) and (12, 0)
3. (12,5)\begin{align*}\left (\frac{-1}{2},5\right )\end{align*} and (32,3)\begin{align*}\left (\frac{3}{2},3\right )\end{align*}
4. (8, 3) and (12, 3)
5. (14, 17) and (–14, –22)
6. (1, 4) and (18, 6)
7. (10, 6) and (10, –6)
8. (–3, 2) and (19, 5)
9. (13, 9) and (2, 9)
10. (10, –1) and (–10, 6)

In 45 – 50, determine the rate of change.

1. Charlene reads 150 pages in 3 hours.
2. Benoit cuts 65 onions in 1.5 hours.
3. Brad drives 215 miles in 3.9 hours.
4. Reece completes 65 jumping jacks in one minute.
5. Harriet is charged \$48.60 for 2,430 text messages.
6. Samuel can eat 65 hotdogs in 22 minutes.

In 51 – 55, identify the slope and the y\begin{align*}y-\end{align*}intercept of each equation.

1. x+y=3\begin{align*}x+y=3\end{align*}
2. 13x=7+y\begin{align*}\frac{1}{3} x=7+y\end{align*}
3. y=25x+3\begin{align*}y=\frac{2}{5} x+3\end{align*}
4. x=4\begin{align*}x=4\end{align*}
5. y=14\begin{align*}y=\frac{1}{4}\end{align*}

In 56 – 60, graph each equation.

1. y=56x1\begin{align*}y=\frac{5}{6} x-1\end{align*}
2. y=x\begin{align*}y=x\end{align*}
3. y=2x+2\begin{align*}y=-2x+2\end{align*}
4. y=38x+5\begin{align*}y=-\frac{3}{8} x+5\end{align*}
5. y=x+4\begin{align*}y=-x+4\end{align*}

In 61 – 63, decide whether the given lines are parallel.

1. 3x+6y=8\begin{align*}3x+6y=8\end{align*} and \begin{align*}y=2x-8\end{align*}
2. \begin{align*}y=x+7\end{align*} and \begin{align*}y=-7-x\end{align*}
3. \begin{align*}2x+4y=16\end{align*} and \begin{align*}y=\frac{-1}{2} x+6\end{align*}

In 64 – 70, evaluate the function for the indicated value.

1. \begin{align*}g(n)= -2|n - 3|;\end{align*} Find \begin{align*}g(7)\end{align*}.
2. \begin{align*}h(a)=a^2-4a\end{align*}; Find \begin{align*}h(8)\end{align*}.
3. \begin{align*}p(t)=3t+1\end{align*}; Find \begin{align*}p\left (\frac{1}{6}\right )\end{align*}.
4. \begin{align*}g(x)=4|x|\end{align*}; Find \begin{align*}g(-3)\end{align*}.
5. \begin{align*}h(n)=\frac{1}{3} n-4\end{align*}; Find \begin{align*}h(24)\end{align*}.
6. \begin{align*}f(x)=\frac{x+8}{6}\end{align*}; Find \begin{align*}f(20)\end{align*}.
7. \begin{align*}r(c)=0.06(c)+c\end{align*}; Find \begin{align*}r(26.99)\end{align*}.
8. The distance traveled by a semi-truck varies directly with the number of hours it has been traveling. If the truck went 168 miles in 4 hours, how many miles will it go in 7 hours?
9. The function for converting Fahrenheit to Celsius is given by \begin{align*}C(F)=\frac{F-32}{1.8}\end{align*}. What is the Celsius equivalent to \begin{align*}84^\circ F\end{align*}?
10. Sheldon started with 32 cookies and is baking more at a rate of 12 cookies/30 minutes. After how many hours will Sheldon have 176 cookies?
11. Mixture \begin{align*}A\end{align*} has a 12% concentration of acid. Mixture \begin{align*}B\end{align*} has an 8% concentration of acid. How much of each mixture do you need to obtain a 60-ounce solution with 12 ounces of acid?
12. The amount of chlorine needed to treat a pool varies directly with its size. If a 5,000-gallon pool needs 5 units of chlorine, how much is needed for a 7,500-gallon pool?
13. The temperature (in Fahrenheit) outside can be predicted by crickets using the rule, “Count the number of cricket chirps in 15 seconds and add 40.” (i) Convert this expression to a function. Call it \begin{align*}T(c)\end{align*}, where \begin{align*}T=\end{align*} temperature and \begin{align*}c=\end{align*} number of chirps in 15 seconds. (ii) Graph this function. (iii) How many chirps would you expect to hear in 15 seconds if the temperature were \begin{align*}67^\circ F\end{align*}? (iv) What does the \begin{align*}y-\end{align*}intercept mean? (v) Are there values for which this graph would not predict well? Why?

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