Chapter 5

Could the table represent the values of a linear function? $$ \begin{array}{c|c|c|c|c|c} \hline x & -6 & -3 & 0 & 3 & 6 \\ \hline y & 12 & 8 & 4 & 0 & -4 \\ \hline \end{array} $$

Solve the systems of equations in Exercises \(1-20\). $$ \left\\{\begin{array}{l} x+y=5 \\ x-y=7 \end{array}\right. $$

Write the linear equations in slopeintercept form \(y=b+m x\). What are the values of \(m\) and \(b\)? $$ y=100-3(x-20) $$

The tuition cost for part-time students taking \(C\) credits at Stonewall College is given by \(300+200 C\) dollars. (a) Find the tuition cost for eight credits. (b) If the tuition cost is \(\$ 1700\), how many credits are taken ?

A homing pigeon starts 1000 miles from home and flies 50 miles toward home each day. Express distance from home in miles, \(D,\) as a function of number of days, \(d\).

Is the expression linear? $$ 5 t-3 $$

Could the table represent the values of a linear function? $$ \begin{array}{l|l|l|l|l|l} \hline x & 7 & 9 & 11 & 13 & 15 \\ \hline y & 43 & 46 & 49 & 52 & 55 \\ \hline \end{array} $$

Solve the systems of equations. $$ \left\\{\begin{array}{l} 3 x+y=10 \\ x+2 y=15 \end{array}\right. $$

A car's value \(t\) years after it is purchased is given by \(V(t)=18,000-1700 t\). How long does it take for the car's value to drop to \(\$ 2000 ?\)

You buy a saguaro cactus \(5 \mathrm{ft}\) high and it grows at a rate of 0.2 inches each year. Express its height in inches, \(h\), as a function of time \(t\) in years since the purchase.

Could the table represent the values of a linear function? $$ \begin{array}{l|l|l|l|l} \hline x & 2 & 4 & 8 & 16 \\ \hline y & 5 & 10 & 15 & 20 \\ \hline \end{array} $$

Solve the systems of equations. $$ \left\\{\begin{array}{l} 3 x-4 y=7 \\ y=4 x-5 \end{array}\right. $$

For the function \(f(t)=\frac{2 t+3}{5}\), (a) Evaluate \(f(11)\) (b) Solve \(f(t)=2\).

The temperature of the soil is \(30^{\circ} \mathrm{C}\) at the surface and decreases by \(0.04^{\circ} \mathrm{C}\) for each centimeter below the surface. Express temperature \(T\) as a function of depth \(d\), in centimeters, below the surface.

Is the expression linear? $$ 6 r+r-1 $$

Could the table represent the values of a linear function? $$ \begin{array}{l|l|l|l|l|l} \hline x & 2 & 4 & 8 & 16 & 32 \\ \hline y & 5 & 7 & 11 & 19 & 35 \\ \hline \end{array} $$

Solve the systems of equations. $$ \left\\{\begin{array}{l} x=y-9 \\ 4 x-y=0 \end{array}\right. $$

Solve \(g(x)=7\) given that \(g(x)=\frac{5 x}{2 x-3} .\)

Give the values for \(b\) and \(m\) for the linear functions in Exercises 4-9. $$ f(x)=3 x+12 $$

Is the expression linear? $$ (3 a+1) / 4 $$

Could the table represent the values of a linear function? $$ \begin{array}{c|c|c|c|c} \hline x & -2 & 0 & 4 & 10 \\ \hline y & 3 & 2 & 0 & -3 \\ \hline \end{array} $$

Solve the systems of equations. $$ \left\\{\begin{array}{l} 2 a+3 b=4 \\ a-3 b=11 \end{array}\right. $$

Graph the equation. $$ y=3 x-6 $$

Company offers three formulas for the weekly salary of its sales people, depending on the number of sales, \(s,\) made each week: (a) \(100+0.10 s\) dollars (b) \(150+0.05 s\) dollars (c) 175 dollars How many sales must be made under option (a) to receive \(\$ 200\) a week?

Give the values for \(b\) and \(m\) for the linear functions. $$ g(t)=250 t-5300 $$

Could the table represent the values of a linear function? Give a formula if it could. $$ \begin{array}{c|c|c|c|c|c|c} \hline t & 0 & 1 & 2 & 3 & 4 & 5 \\ \hline Q & 100.00 & 95.01 & 90.05 & 85.11 & 80.20 & 75.31 \\ \hline \end{array} $$

Solve the systems of equations. $$ \left\\{\begin{array}{l} 3 w-z=4 \\ w+2 z=6 \end{array}\right. $$

Graph the equation. $$ y=5 $$

Give the values for \(b\) and \(m\) for the linear functions. $$ h(n)=0.01 n+100 $$

Could the table represent the values of a linear function? Give a formula if it could. $$ \begin{array}{c|c|c|c|c|c|c} \hline t & 3 & 7 & 19 & 21 & 26 & 42 \\ \hline Q & 5.79 & 6.67 & 9.31 & 9.75 & 10.85 & 14.37 \\ \hline \end{array} $$

Solve the systems of equations. $$ \left\\{\begin{array}{l} 2 p+3 r=10 \\ -5 p+2 r=13 \end{array}\right. $$

Graph the equation. $$ 2 x-3 y=24 $$

Company offers three formulas for the weekly salary of its sales people, depending on the number of sales, \(s,\) made each week: (a) \(100+0.10 s\) dollars (b) \(150+0.05 s\) dollars (c) 175 dollars At what sales level do options (a) and (b) produce the same salary?

Is the expression linear? $$ 4^{2}+(1 / 3) x $$

Could the table represent the values of a linear function? Give a formula if it could. $$ \begin{array}{c|c|c|c|c} \hline x & 0 & 2 & 10 & 20 \\ \hline y & 50 & 58 & 90 & 130 \\ \hline \end{array} $$

Solve the systems of equations. $$ \left\\{\begin{array}{l} 5 d+4 e=2 \\ 4 d+5 e=7 \end{array}\right. $$

Graph the equation. $$ x=7 $$

Company offers three formulas for the weekly salary of its sales people, depending on the number of sales, \(s,\) made each week: (a) \(100+0.10 s\) dollars (b) \(150+0.05 s\) dollars (c) 175 dollars At what sales level do options (b) and (c) produce the same salary?

Give the values for \(b\) and \(m\) for the linear functions. $$ w(c)=0.5 c $$

Is the expression linear? $$ 6 A-3(1-3 A) $$

(a) Write a constraint equation. (b) Choose two solutions. (c) Graph the equation and mark your solutions. The relation between quantity of chicken and quantity of steak if chicken costs \(\$ 1.29 / \mathrm{lb}\) and steak costs \(\$ 3.49 / \mathrm{lb},\) and you have \(\$ 100\) to spend on a barbecue.

Solve the systems of equations. $$ \left\\{\begin{aligned} 8 x-3 y &=7 \\ 4 x+y &=11 \end{aligned}\right. $$

Graph the equation. $$ y=-\frac{2}{3} x-4 $$

Company offers three formulas for the weekly salary of its sales people, depending on the number of sales, \(s,\) made each week: (a) \(100+0.10 s\) dollars (b) \(150+0.05 s\) dollars (c) 175 dollars At what sales level do options (a) and (c) produce the same salary?

For each of the linear expressions in \(x\) in exercises. give the constant term and the coefficient of \(x\). $$ 3 x+4 $$

Solve the systems of equations. $$ \left\\{\begin{aligned} 4 w+5 z &=11 \\ z-2 w &=5 \end{aligned}\right. $$

Graph the equation. $$ y=200-4 x $$

Solve the equations. $$ 7-3 y=-17 $$

The cost, \(\$ C\), of hiring a repairman for \(h\) hours is given by \(C=50+25 h\) (a) What does the repairman charge to walk in the door? (b) What is his hourly rate?

For each of the linear expressions in \(x\) in exercises. give the constant term and the coefficient of \(x\). $$ 5 x-x+5 $$