Chapter 2

Find the slope of the line through \(P\) and \(Q .\) \(P(0,0), Q(4,2)\)

Plot the given points in a coordinate plane: $$ (2,3),(-2,3),(4,5),(4,-5),(-4,5),(-4,-5) $$

Use a graphing calculator or computer to decide which viewing rectangle \((\mathrm{a})-(\mathrm{d})\) produces the most appropriate graph of the equation. $$\begin{array}{l}{y=x^{4}+2} \\ {\text { (a) }[-2,2] \text { by }[-2,2]} \\\ {\text { (b) }[0,4] \text { by }[0,4]} \\ {\text { (c) }[-8,8] \text { by }[-4,40]} \\ {\text { (d) }[-40,40] \text { by }[-80,800]}\end{array}$$

1–6 ? Determine whether the given points are on the graph of the equation. $$ y=3 x-2 ; \quad(0,2),\left(\frac{1}{3}, 1\right),(1,1) $$

1–12 ? Write an equation that expresses the statement. \(P\) is directly proportional to \(w\)

Find the slope of the line through \(P\) and \(Q .\) \(P(0,0), Q(2,-6)\)

Use a graphing calculator or computer to decide which viewing rectangle \((\mathrm{a})-(\mathrm{d})\) produces the most appropriate graph of the equation. $$ \begin{array}{l}{y=x^{2}+7 x+6} \\ {\text { (a) }[-5,5] \text { by }[-5,5]} \\\ {\text { (b) }[0,10] \text { by }[-20,100]} \\ {\text { (c) }[-15,8] \text { by }[-20,100]} \\ {\text { (d) }[-10,3] \text { by }[-100,20]}\end{array} $$

1–6 ? Determine whether the given points are on the graph of the equation. $$ y=\sqrt{x+1} ; \quad(1,0),(0,1),(3,2) $$

1–12 ? Write an equation that expresses the statement. \(\nu\) is inversely proportional to \(z\)

Find the slope of the line through \(P\) and \(Q .\) \(P(2,2), Q(-10,0)\)

Use a graphing calculator or computer to decide which viewing rectangle \((\mathrm{a})-(\mathrm{d})\) produces the most appropriate graph of the equation. $$ \begin{array}{l}{y=100-x^{2}} \\ {\text { (a) }[-4,4] \text { by }[-4,4]} \\\ {\text { (b) }[-10,10] \text { by }[-10,10]} \\ {\text { (c) }[-15,15] \text { by }[-30,110]} \\ {\text { (d) }[-4,4] \text { by }[-30,110]}\end{array} $$

1–6 ? Determine whether the given points are on the graph of the equation. $$ x-2 y-1=0 ; \quad(0,0),(1,0),(-1,-1) $$

1–12 ? Write an equation that expresses the statement. \(w\) is jointly proportional to \(m\) and \(n\)

Find the slope of the line through \(P\) and \(Q .\) \(P(1,2), Q(3,3)\)

Use a graphing calculator or computer to decide which viewing rectangle \((\mathrm{a})-(\mathrm{d})\) produces the most appropriate graph of the equation. $$ \begin{array}{l}{y=2 x^{2}-1000} \\ {\text { (a) }[-10,10] \text { by }[-10,10]} \\ {\text { (b) }[-10,10] \text { by }[-100,100]} \\ {\text { (c) }[-10,10] \text { by }[-1000,1000]} \\ {\text { (d) }[-25,25] \text { by }[-1200,200]}\end{array} $$

1–6 ? Determine whether the given points are on the graph of the equation. $$ y\left(x^{2}+1\right)=1 ; \quad(1,1),\left(1, \frac{1}{2}\right),\left(-1, \frac{1}{2}\right) $$

1–12 ? Write an equation that expresses the statement. \(y\) is proportional to \(s\) and inversely proportional to \(t.\)

Find the slope of the line through \(P\) and \(Q .\) \(P(2,4), Q(4,3)\)

Use a graphing calculator or computer to decide which viewing rectangle \((\mathrm{a})-(\mathrm{d})\) produces the most appropriate graph of the equation. $$ \begin{array}{l}{y=10+25 x-x^{3}} \\ {\text { (a) }[-4,4] \text { by }[-4,4]} \\\ {\text { (b) }[-10,10] \text { by }[-10,10]} \\ {\text { (c) }[-20,20] \text { by }[-100,100]} \\ {\text { (d) }[-100,100] \text { by }[-200,200]}\end{array} $$

1–6 ? Determine whether the given points are on the graph of the equation. $$ x^{2}+x y+y^{2}=4 ; \quad(0,-2),(1,-2),(2,-2) $$

1–12 ? Write an equation that expresses the statement. \(P\) varies inversely as \(T.\)

Find the slope of the line through \(P\) and \(Q .\) \(P(2,-5), Q(-4,3)\)

Use a graphing calculator or computer to decide which viewing rectangle \((\mathrm{a})-(\mathrm{d})\) produces the most appropriate graph of the equation. $$ \begin{array}{l}{y=\sqrt{8 x-x^{2}}} \\ {\text { (a) }[-4,4] \text { by }[-4,4]} \\ {\text { (b) }[-5,5] \text { by }[0,100]} \\ {\text { (c) }[-10,10] \text { by }[-10,40]} \\ {\text { (d) }[-2,10] \text { by }[-2,6]}\end{array} $$

1–6 ? Determine whether the given points are on the graph of the equation. $$ x^{2}+y^{2}=1 ; \quad(0,1),\left(\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}\right),\left(\frac{\sqrt{3}}{2}, \frac{1}{2}\right) $$

1–12 ? Write an equation that expresses the statement. \(z\) is proportional to the square root of \(y.\)

Find the slope of the line through \(P\) and \(Q .\) \(P(1,-3), Q(-1,6)\)

\(7-14\) A pair of points is graphed. (a) Plot the points in a coordinate plane. (b) Find the distance between them. (c) Find the midpoint of the segment that joins them. $$ (0,8),(6,16) $$

7–10 ? An equation and its graph are given. Find the x- and y-intercepts. $$ y=4 x-x^{2} $$

1–12 ? Write an equation that expresses the statement. A is proportional to the square of \(t\) and inversely proportional to the cube of \(x .\)

Find the slope of the line through \(P\) and \(Q .\) \(P(-1,-4), Q(6,0)\)

\(7-14\) A pair of points is graphed. (a) Plot the points in a coordinate plane. (b) Find the distance between them. (c) Find the midpoint of the segment that joins them. $$ (-2,5),(10,0) $$

7–10 ? An equation and its graph are given. Find the x- and y-intercepts. $$ \frac{x^{2}}{9}+\frac{y^{2}}{4}=1 $$

1–12 ? Write an equation that expresses the statement. \(V\) is jointly proportional to \(I, w,\) and \(h.\)

\(7-14\) A pair of points is graphed. (a) Plot the points in a coordinate plane. (b) Find the distance between them. (c) Find the midpoint of the segment that joins them. $$ (-3,-6),(4,18) $$

7–10 ? An equation and its graph are given. Find the x- and y-intercepts. $$ x^{4}+y^{2}-x y=16 $$

1–12 ? Write an equation that expresses the statement. \(S\) is jointly proportional to the squares of \(r\) and \(\theta.\)

(a) Sketch lines through \((0,0)\) with slopes \(1,0, \frac{1}{2}, 2,\) and \(-1 .\) (b) Sketch lines through \((0,0)\) with slopes \(\frac{1}{3}, \frac{1}{2},-\frac{1}{3},\) and 3

\(7-14\) A pair of points is graphed. (a) Plot the points in a coordinate plane. (b) Find the distance between them. (c) Find the midpoint of the segment that joins them. $$ (-1,-1),(9,9) $$

7–10 ? An equation and its graph are given. Find the x- and y-intercepts. $$ x^{2}+y^{3}-x^{2} y^{2}=64 $$

1–12 ? Write an equation that expresses the statement. \(R\) is proportional to \(i\) and inversely proportional to \(P\) and \(t.\)

\(7-14\) A pair of points is graphed. (a) Plot the points in a coordinate plane. (b) Find the distance between them. (c) Find the midpoint of the segment that joins them. $$ (6,-2),(-1,3) $$

11–18 ? Find the x- and y-intercepts of the graph of the equation. $$ y=x-3 $$

1–12 ? Write an equation that expresses the statement. \(A\) is jointly proportional to the square roots of \(x\) and \(y.\)

\(7-14\) A pair of points is graphed. (a) Plot the points in a coordinate plane. (b) Find the distance between them. (c) Find the midpoint of the segment that joins them. $$ (-1,6),(-1,-3) $$

Determine an appropriate viewing rectangle for the equation and use it to draw the graph. $$ y=\sqrt{12 x-17} $$

11–18 ? Find the x- and y-intercepts of the graph of the equation. $$ y=x^{2}-5 x+6 $$

13–22 ? Express the statement as an equation. Use the given information to find the constant of proportionality. \(y\) is directly proportional to \(x .\) If \(x=6,\) then \(y=42.\)

\(7-14\) A pair of points is graphed. (a) Plot the points in a coordinate plane. (b) Find the distance between them. (c) Find the midpoint of the segment that joins them. $$ (3,4),(-3,-4) $$

11–18 ? Find the x- and y-intercepts of the graph of the equation. $$ y=x^{2}-9 $$

13–22 ? Express the statement as an equation. Use the given information to find the constant of proportionality. \(z\) varies inversely as \(t .\) If \(t=3,\) then \(z=5.\)