5.9: Chapter 5 Review
Find an equation of the line in slope-intercept form using the given information.
- (3, 4) with \begin{align*}slope= \frac{2}{3}\end{align*}
slope=23 - \begin{align*}slope=-5\end{align*}, \begin{align*}y-intercept=9\end{align*}
- \begin{align*}slope=-1\end{align*} containing (6, 0)
- containing (3.5, 1) and (9, 6)
- \begin{align*}slope = 3\end{align*}, \begin{align*}y-\end{align*}intercept \begin{align*}=-1\end{align*}
- \begin{align*}slope=\frac{-1}{3}\end{align*} containing (–3, –4)
- containing (0, 0) and (9, –8)
- \begin{align*}slope=\frac{5}{3}\end{align*}, \begin{align*}y-\end{align*}intercept \begin{align*}=6\end{align*}
- containing (5, 2) and (–6, –3)
- \begin{align*}slope=3\end{align*} and \begin{align*}f(6)=1\end{align*}
- \begin{align*}f(2)=-5\end{align*} and \begin{align*}f(-6)=3\end{align*}
- \begin{align*}slope=\frac{3}{8}\end{align*} and \begin{align*}f(1)=1\end{align*}
Find an equation of the line in point-slope form using the given information.
- \begin{align*}slope=m\end{align*} containing \begin{align*}(x_1, y_1)\end{align*}
- \begin{align*}slope=\frac{1}{2}\end{align*} containing (-7, 5)
- \begin{align*}slope=2\end{align*} containing (7, 0)
Graph the following equations.
- \begin{align*}y+3=-(x-2)\end{align*}
- \begin{align*}y-7=\frac{-2}{3} (x+5)\end{align*}
- \begin{align*}y+1.5=\frac{3}{2}(x+4)\end{align*}
Find the equation of the line represented by the function below in point-slope form.
- \begin{align*}f(1)=-3\end{align*} and \begin{align*}f(6)=0\end{align*}
- \begin{align*}f(9)=2\end{align*} and \begin{align*}f(9)=-5\end{align*}
- \begin{align*}f(2)=0\end{align*} and \begin{align*}slope=\frac{8}{3}\end{align*}
Write the standard form of the equation of each line.
- \begin{align*}y-3=\frac{-1}{4}(x+4)\end{align*}
- \begin{align*}y=\frac{2}{7}(x-21)\end{align*}
- \begin{align*}-3x-25=5y\end{align*}
Write the standard form of the line for each equation using the given information.
- containing (0, –4) and (–1, 5)
- \begin{align*}slope=\frac{4}{3}\end{align*} containing (3, 2)
- \begin{align*}slope=5\end{align*} containing (5, 0)
- Find the slope and \begin{align*}y-\end{align*}intercept of \begin{align*}7x+5y=16\end{align*}.
- Find the slope and \begin{align*}y-\end{align*}intercept of \begin{align*}7x-7y=-14\end{align*}.
- Are \begin{align*}\frac{1}{2} x+\frac{1}{2} y=5\end{align*} and \begin{align*}2x+2y=3\end{align*} parallel, perpendicular, or neither?
- Are \begin{align*}x=4\end{align*} and \begin{align*}y=-2\end{align*} parallel, perpendicular, or neither?
- Are \begin{align*}2x+8y=26\end{align*} and \begin{align*}x+4y=13\end{align*} parallel, perpendicular, or neither?
- Write an equation for the line perpendicular to \begin{align*}y=3x+4\end{align*} containing (–5, 1).
- Write an equation for the line parallel to \begin{align*}y=x+5\end{align*} containing (–4, –4).
- Write an equation for the line perpendicular to \begin{align*}9x+5y=25\end{align*} containing (–4, 4).
- Write an equation for the line parallel to \begin{align*}y=5\end{align*} containing (–7, 16).
- Write an equation for the line parallel to \begin{align*}x=0\end{align*} containing (4, 6).
- Write an equation for the line perpendicular to \begin{align*}y=-2\end{align*} containing (10, 10).
- An Internet café charges $6.00 to use 65 minutes of their Wifi. It charges $8.25 to use 100 minutes. Suppose the relationship is linear.
- Write an equation to model this data in point-slope form.
- What is the price to acquire the IP address?
- How much does the café charge per minute?
- A tomato plant grows \begin{align*}\frac{1}{2}\end{align*} inch per week. The plant was 5 inches tall when planted.
- Write an equation in slope-intercept form to represent this situation.
- How many weeks will it take the plant to reach 18 inches tall?
- Joshua bought a television and paid 6% sales tax. He then bought an albino snake and paid 4.5% sales tax. His combined purchases totaled $679.25.
- Write an equation to represent Joshua’s purchases.
- Graph all the possible solutions to this situation.
- Give three examples that would be solutions to this equation.
- Comfy Horse Restaurant began with a 5-gallon bucket of dishwashing detergent. Each day \begin{align*}\frac{1}{4}\end{align*} gallon is used.
- Write an equation to represent this situation in slope-intercept form.
- How long will it take to empty the bucket?
- The data below shows the divorce rate per 1,000 people in the state of Wyoming for various years (source: Nation Masters).
- Graph the data in a scatter plot.
- Fit a line to the data by hand.
- Find the line of best fit by hand.
- Using your model, what do you predict the divorce rate is in the state of Wyoming in the year 2011?
- Repeat this process using your graphing calculator. How close was your line to the one the calculator provided?
\begin{align*}&\text{Year} && 2000 && 2001 && 2002 && 2003 && 2004 && 2005 && 2006 && 2007\\ &\text{Rate (per 1,000 people)} && 5.8 && 5.8 && 5.4 && 5.4 && 5.3 && 5.4 && 5.3 && 5.0\end{align*}
- The table below shows the percentage of voter turnout at presidential elections for various years (source The American Presidency Project).
\begin{align*}&\text{Year} && 1828 && 1844 && 1884 && 1908 && 1932 && 1956 && 1972 && 1988 && 2004\\ &\% \ \text{of Voter Turnout} && 57.6 && 78.9 && 77.5 && 65.4 && 56.9 && 60.6 && 55.21 && 50.15 && 55.27\end{align*}
(a) Draw a scatter plot of this data.
(b) Use the linear regression feature on your calculator to determine a line of best fit and draw it on your graph.
(c) Use the line of best fit to predict the voter turnout for the 2008 election.
(d) What are some outliers to this data? What could be a cause for these outliers?
- The data below shows the bacteria population in a Petri dish after \begin{align*}h\end{align*} hours.
\begin{align*}&h \ \text{hours} && 0 && 1 && 2 && 3 && 4 && 5 && 6\\ &\text{Bacteria present} && 100 && 200 && 400 && 800 && 1600 && 3200 && 6400\end{align*}
(a) Use the method of interpolation to find the number of bacteria present after 4.25 hours.
(b) Use the method of extrapolation to find the number of bacteria present after 10 hours.
(c) Could this data be best modeled with a linear equation? Explain your answer.
- How many seconds are in 3 months?
- How many inches are in a kilometer?
- How many cubic inches are in a gallon of milk?
- How many meters are in 100 acres?
- How many fathoms is 616 feet?