Chapter 1

Write equation in the form \(y=m x+b .\) (A suggested window for a comprehensive graph of the equation is given. \(-0.23 x-0.46 y=0.82\) \([-5,5]\) by \([-5,5]\)

In Exercises \(37-40,\) find the constant of variation \(k\) and the undetermined value in the table if \(y\) is directly proportional to \(x\). Cost \(y\) of buying \(x\) compact discs having the same price \begin{tabular}{c|c|c|c} \(x\) & 3 & 4 & 5 \\ \hline\(y\) & \(\$ 41.97\) & \(\$ 55.96\) & \(?\) \end{tabular}

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

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

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

Write equation in the form \(y=m x+b .\) (A suggested window for a comprehensive graph of the equation is given. \(1.2 x+1.6 y=5.0\) \([-6,6]\) by \([-4,4]\)

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?

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

Write equation in the form \(y=m x+b .\) (A suggested window for a comprehensive graph of the equation is given. \(2 y-5 x=0\) \([-10,10]\) by \([-10,10]\)

Solve each problem. Rate of Nerve Impulses The rate at which impulses are transmitted along a nerve fiber is directly proportional to the diameter of the fiber. The rate for a certain fiber is 40 meters per second when the diameter is 6 micrometers. Find the rate if the diameter is 8 micrometers.

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

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

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. $$4(0.23 x+\sqrt{5})=\sqrt{2} x+1$$

Find the slope (if defined) of the line that passes through the given points. $$44 .(-8,2) \text { and }(-8,1)$$

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

Solve each problem. Strength of a Beam The maximum load that a horizontal beam can carry is directly proportional to its width. If a beam 1.5 inches wide can support a load of 250 pounds, find the load that a beam of the same type can support if its width is 3.5 inches. What is the constant of variation? (IMAGE CAN'T COPY)

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 slope (if defined) of the line that passes through the given points. $$44 .(-8,2) \text { and }(-8,1)$$

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

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 satisfying the given conditions, giving it in slope-intercept form if possible. Through \((-2,0),\) perpendicular to \(8 x-3 y=7\)

Solve each problem. Volume of Water \(\quad\) 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. (IMAGE CAN'T COPY)

Use the intersection-of-graphs method to approximate each solution to the nearest hundredth. $$3 \pi x-\sqrt[4]{3}=0.75 \pi x+\sqrt{19}$$

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) \end{aligned}

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

Solve each problem. Height of a Tree A certain tree casts a shadow 45 feet long. At the same time, the shadow cast by a vertical stick 2 feet high is 1.75 feet long. How tall is the tree? (Hint: Use similar triangles.) (IMAGE CAN'T COPY)

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

Given an equation having \(x\) and \(y\) as variables, explain how to determine the \(x\) - and \(y\) -intercepts.

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

Solve each problem. Height of a Streetlight 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. $$\begin{aligned} &[-40,40] \text { by }[-30,30]\\\ &\mathrm{Xscl}=5 \quad \mathrm{Yscl}=5 \end{aligned}$$

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 satisfying the given conditions, giving it in slope-intercept form if possible. Through \((-5,8),\) parallel to \(y=-0.2 x+6\)

Set the viewing window of your calculator to the given specifications. Make a sketch of your window. $$\begin{aligned} &[-5,10] \text { by }[-5,10]\\\ &\mathrm{Xscl}=3 \quad \mathrm{Yscl}=3 \end{aligned}$$

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 satisfying the given conditions, 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. $$\begin{aligned} &[-3.5,3.5] \text { by }[-4,10]\\\ &\mathrm{Xscl}=1 \quad \mathrm{Yscl}=1 \end{aligned}$$

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 satisfying the given conditions, giving it in slope-intercept form if possible. Through the origin, perpendicular to \(2 x+y=6\)

Solve each problem. Biologists use direct variation to estimate the number of individuals of a species in a particular area. They first capture a sample of individuals from the area and mark each specimen with a harmless tag. Later, they return and capture another sample from the same area. They base their estimate on the theory that the proportion of tagged specimens in the new sample is the same as the proportion of tagged individuals in the entire area. Use this idea to work Exercises 51 and 52 . Estimating Fish in a Lake Biologists tagged and released 250 trout. On a later date, they found 7 tagged trout in a sample of \(350 .\) Estimate, to the nearest hundred, the total number of trout in the lake. (IMAGE CAN'T COPY)

Set the viewing window of your calculator to the given specifications. Make a sketch of your window. $$\begin{aligned} &[-100,100] \text { by }[-50,50]\\\ &\mathrm{Xscl}=20 \quad \mathrm{Yscl}=25 \end{aligned}$$

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. $$6(2 x+1)=4 x+8\left(x+\frac{3}{4}\right)$$

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

Solve each problem. Biologists use direct variation to estimate the number of individuals of a species in a particular area. They first capture a sample of individuals from the area and mark each specimen with a harmless tag. Later, they return and capture another sample from the same area. They base their estimate on the theory that the proportion of tagged specimens in the new sample is the same as the proportion of tagged individuals in the entire area. Use this idea to work Exercises 51 and 52 . 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. (Source: "Estimating the Size of Wildlife Populations," Chatterjee, S., in Statistics by Example, obtained from data in Transactions of the American Fisheries Society.)

Set the viewing window of your calculator to the given specifications. Make a sketch of your window. $$\begin{aligned} &[-4.7,4.7] \text { by }[-3.1,3.1]\\\ &\mathbf{X s c l}=1 \quad \mathbf{Y s c l}=1 \end{aligned}$$

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. $$3(x+2)-5(x+2)=-2 x-4$$

Find \(f(x)\) at the indicated value of \(x\). $$f(x)=3 x-4, x=-2$$

Find the equation of the line satisfying the given conditions, giving it in slope-intercept form if possible. Perpendicular to \(x=3,\) passing through \((1,2)\)