Chapter 1

Write each equation in the form \(y=m x+b .\) (A suggested window for a comprehensive graph of the equation is given. $$\begin{aligned} &-2 x+7 y=4\\\ &[-5,5] \text { by }[-5,5] \end{aligned}$$

Find the slope (if defined) of the line that passes through the given points. $$(-2,1) \text { and }(3,6)$$

find the constant of variation \(k\) and the undetermined value in the table if \(y\) is directly proportional to \(x\). Sales tax \(y\) on a purchase of \(x\) dollars \begin{tabular}{|c|c|c|c|} \hline\(x\) & \(\$ 25\) & 555 & \(?\) \\ \hline\(y\) & \(\$ 1.50\) & \(\$ 3.30\) & \(\$ 5.10\) \end{tabular}

If the \(x\) -coordinate of a point is \(0,\) on which axis must the point lie?

Solve each equation analytically. Check it analytically, and then support the solution graphically. $$-[x-(4 x+2)]=2+(2 x+7)$$

Write each equation in the form \(y=m x+b .\) (A suggested window for a comprehensive graph of the equation is given. $$\begin{aligned} &-0.23 x-0.46 y=0.82\\\ &[-5,5] \text { by }[-5,5] \end{aligned}$$

Find the slope (if defined) of the line that passes through the given points. $$(-2,3) \text { and }(-1,2)$$

If the \(y\) -coordinate of a point is \(0,\) on which axis must the point lie?

Write each equation in the form \(y=m x+b .\) (A suggested window for a comprehensive graph of the equation is given. $$\begin{aligned} &-0.23 x-0.46 y=0.82\\\ &[-5,5] \text { by }[-5,5] \end{aligned}$$$$\begin{aligned} &1.2 x+1.6 y=5.0\\\ &[-6,6] \text { by }[-4,4] \end{aligned}$$

Find the slope (if defined) of the line that passes through the given points. \((8,4)\) and \((-1,-3)\)

Solve each problem. Pressure of a Liquid The pressure exerted by a certain liquid at a given point is directly proportional to the depth of the point beneath the surface of the liquid. If the pressure exerted at 30 feet is 13 pounds per square inch, what is the pressure exerted at 70 feet?

Write each equation in the form \(y=m x+b .\) (A suggested window for a comprehensive graph of the equation is given. $$\begin{aligned} &2 y-5 x=0\\\ &[-10,10] \text { by }[-10,10] \end{aligned}$$

Find the slope (if defined) of the line that passes through the given points. $$(-4,-3) \text { and }(5,0)$$

Solve each problem. Cost of Tuition The cost of tuition is directly proportional to the number of credits taken. If 11 credits cost \(\$ 720.50,\) find the cost of taking 16 credits. What is the constant of variation?

Find the equation of the line described, giving it in slope-intercept form if possible. Through \((-1,4),\) parallel to \(x+3 y=5\)

Find the slope (if defined) of the line that passes through the given points. $$(-11,3) \text { and }(-11,5)$$

Solve each problem. cost of Tuition The cost of tuition is directly proportional to the number of credits taken. If 11 credits cost \(\$ 720.50,\) find the cost of taking 16 credits. What is the constant of variation?

Use the intersection-of-graphs method to approximate each solution to the nearest hundredth. $$9(-0.84 x+\sqrt{17})=\sqrt{6} x-4$$

Find the equation of the line described, giving it in slope-intercept form if possible. Through \((3,-2),\) parallel to \(2 x-y=5\)

Find the slope (if defined) of the line that passes through the given points. $$(-8,2) \text { and }(-8,1)$$

Use the intersection-of-graphs method to approximate each solution to the nearest hundredth. $$2 \pi x+\sqrt[3]{4}=0.5 \pi x-\sqrt{28}$$

Find the equation of the line described, giving it in slope-intercept form if possible. Through \((1,6),\) perpendicular to \(3 x+5 y=1\)

Find the slope (if defined) of the line that passes through the given points. $$\left(\frac{2}{3}, 9\right) \text { and }\left(\frac{1}{2}, 9\right)$$

Find the equation of the line described, giving it in slope-intercept form if possible. Through \((-2,0)\), perpendicular to \(8 x-3 y=7\)

Find the slope (if defined) of the line that passes through the given points. $$(0.12,0.36) \text { and }(0.18,0.36)$$

Solve each problem. Volume of Water \(\mathbf{A}\) water tank in the shape of an inverted cone has height 6 feet and radius 2 feet. If the water level in the tank is 3.5 feet, calculate the volume of the water.

Use the intersection-of-graphs method to approximate each solution to the nearest hundredth. $$0.23(\sqrt{3}+4 x)-0.82(\pi x+2.3)=5$$

Find the equation of the line described, giving it in slope-intercept form if possible. Through \((-5,7)\), perpendicular to \(y=-2\)

Find the slope (if defined) of the line that passes through the given points. $$\left(\frac{1}{2},-\frac{2}{3}\right) \text { and }\left(-\frac{3}{4}, \frac{1}{6}\right)$$

Set the viewing window of your calculator to the given specifications. Make a sketch of your window. $$\begin{aligned} &[-10,10] \text { by }[-10,10]\\\ &\mathrm{Xscl}=1 \quad \mathrm{Yscl}=1 \end{aligned}$$

Use the intersection-of-graphs method to approximate each solution to the nearest hundredth. $$-0.15(6+\sqrt{2} x)+1.4(2 \pi x-6.1)=10$$

Find the equation of the line described, giving it in slope-intercept form if possible. Through \((1,-4),\) perpendicular to \(x=4\)

Solve each problem. Height of a Streethght A person 66 inches tall is standing 15 feet from a streetlight. If the person casts a shadow 84 inches long, how tall is the streetlight?

Set the viewing window of your calculator to the given specifications. Make a sketch of your window. $$\begin{aligned} &[-40,40] \text { by }[-30,30]\\\ &\mathrm{Xscl}=5 \quad \mathrm{Yscl}=5 \end{aligned}$$

Classify each equation as a contradiction, an identity, or a conditional equation. Give the solution set. Use a graph or table to support your answer. $$5 x+5=5(x+3)-3$$

Find the equation of the line described, giving it in slope-intercept form if possible. Through \((-5,8),\) parallel to \(y=-0.2 x+6\)

Solve each problem. Hooke's Law If a 3 -pound weight stretches a spring 2.5 inches, how far will a 17 -pound weight stretch the spring?

Set the viewing window of your calculator to the given specifications. Make a sketch of your window. $$\begin{aligned} &[-6,10] \text { by }[-6,10]\\\ &\mathrm{Xscl}=1 \quad \mathrm{Yscl}=1 \end{aligned}$$

Classify each equation as a contradiction, an identity, or a conditional equation. Give the solution set. Use a graph or table to support your answer. $$5-4 x=5 x-(9+9 x)$$

Find the equation of the line described, giving it in slope-intercept form if possible. Through \((-4,-7),\) parallel to \(x+y=5\)

Solve each problem. Hooke's Law If a 9.8 -pound weight stretches a spring 0.75 inch, how much weight would be needed to stretch the spring 3.1 inches?

Set the viewing window of your calculator to the given specifications. Make a sketch of your window. $$\begin{aligned} &[-3.5,3.5] \text { by }[-4,10]\\\ &\mathrm{Xscl}=1 \quad \mathrm{Yscl}=1 \end{aligned}$$

Find the equation of the line described, giving it in slope-intercept form if possible. Through the origin, perpendicular to \(2 x+y=6\)

Set the viewing window of your calculator to the given specifications. Make a sketch of your window. $$\begin{aligned} &[0,10] \text { by }[0,400]\\\ &\mathrm{Xscl}=1 \quad \mathrm{Yscl}=100 \end{aligned}$$

Classify each equation as a contradiction, an identity, or a conditional equation. Give the solution set. Use a graph or table to support your answer. $$3(x+2)-5(x+2)=-2 x-4$$

If the graph of \(y=m x+b\) falls from left to right and intersects the \(y\) -axis below the origin, then which of the following is true? A. \(m>0, b>0\) B. \(m>0, b<0\) C .\(m<0, b>0\) D. \(m<0, b<0\)

Find the equation of the line described, giving it in slope-intercept form if possible. Through the origin, parallel to \(y=-3.5 x+7.4\)

Solve each problem. Estimating Seal Pups in a Breeding Area According to an actual survey in \(1961,\) to estimate the number of seal pups in a certain breeding area in Alaska, 4963 pups were tagged in early August. In late August, a sample of 900 pups was examined and 218 of these were found to have been tagged. Use this information to estimate, to the nearest hundred, the total number of seal pups in this breeding area.

Set the viewing window of your calculator to the given specifications. Make a sketch of your window. $$\begin{aligned} &[-6.6,6.6] \text { by }[-4.1,4.1]\\\ &\mathrm{Xscl}=1 \quad \mathrm{Yscl}=1 \end{aligned}$$

Classify each equation as a contradiction, an identity, or a conditional equation. Give the solution set. Use a graph or table to support your answer. $$7 x-3[5 x-(5+x)]=1-4 x$$