Chapter 2

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

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

\(11-36\) Make a table of values and sketch the graph of the equation. Find the \(x\) - and \(y\) -intercepts. $$ y=2 x $$

Sketch the region given by the set. \(\\{(x, y) | 0 \leq y \leq 4\\}\)

\(11-22\) a Determine an appropriate viewing rectangle for the equation, and use it to draw the graph. $$ y=4+6 x-x^{2} $$

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

\(11-36\) Make a table of values and sketch the graph of the equation. Find the \(x\) - and \(y\) -intercepts. $$ y=-x+4 $$

Sketch the region given by the set. \(\\{(x, y) | x y<0\\}\)

(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.

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

\(11-36\) Make a table of values and sketch the graph of the equation. Find the \(x\) - and \(y\) -intercepts. $$ y=3 x+3 $$

Sketch the region given by the set. \(\\{(x, y) | x y>0\\}\)

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

\(11-36\) Make a table of values and sketch the graph of the equation. Find the \(x\) - and \(y\) -intercepts. $$ 2 x-y=6 $$

Sketch the region given by the set. \(\\{(x, y) | x \geq 1 \text { and } y<3\\}\)

\(11-22\) a Determine an appropriate viewing rectangle for the equation, and use it to draw the graph. $$ y=\sqrt{12 x-17} $$

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

\(11-36\) Make a table of values and sketch the graph of the equation. Find the \(x\) - and \(y\) -intercepts. $$ x+y=3 $$

Sketch the region given by the set. \(\\{(x, y) |-2< x< 2 \text { and } y \geq 3\\}\)

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 \(y=42\)

\(11-36\) Make a table of values and sketch the graph of the equation. Find the \(x\) - and \(y\) -intercepts. $$ y=1-x^{2} $$

Sketch the region given by the set. \(\\{(x, y)| | x |>4\\}\)

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 \(z=5\)

\(11-36\) Make a table of values and sketch the graph of the equation. Find the \(x\) - and \(y\) -intercepts. $$ y=x^{2}+2 $$

Sketch the region given by the set. \(\\{(x, y)| | y | \leq 2\\}\)

Find an equation of the line that satisfies the given conditions. Through \((2,3) ;\) slope 5

Express the statement as an equation. Use the given information to find the constant of proportionality. \(R\) is inversely proportional to \(s .\) If \(s=4,\) then \(R=3\)

\(11-36\) Make a table of values and sketch the graph of the equation. Find the \(x\) - and \(y\) -intercepts. $$ 4 y=x^{2} $$

Sketch the region given by the set. \(\\{(x, y)| | x | \leq 2 \text { and }|y| \leq 3\\}\)

Find an equation of the line that satisfies the given conditions. Through \((-2,4) ;\) slope \(-1\)

Express the statement as an equation. Use the given information to find the constant of proportionality. \(P\) is directly proportional to \(T .\) If \(T=300,\) then \(P=20\)

\(11-22\) a Determine an appropriate viewing rectangle for the equation, and use it to draw the graph. $$ y=\frac{x}{x^{2}+25} $$

\(11-36\) Make a table of values and sketch the graph of the equation. Find the \(x\) - and \(y\) -intercepts. $$ 8 y=x^{3} $$

Sketch the region given by the set. \(\\{(x, y)| | x |>2 \text { and }|y|>3\\}\)

Find an equation of the line that satisfies the given conditions. Through \((1,7) ;\) slope \(\frac{2}{3}\)

Express the statement as an equation. Use the given information to find the constant of proportionality. M varies directly as \(x\) and inversely as \(y .\) If \(x=2\) and \(y=6\) , then \(M=5\)

\(11-36\) Make a table of values and sketch the graph of the equation. Find the \(x\) - and \(y\) -intercepts. $$ y=x^{2}-9 $$

Find an equation of the line that satisfies the given conditions. Through \((-3,-5) ;\) slope \(-\frac{7}{2}\)

Express the statement as an equation. Use the given information to find the constant of proportionality. \(S\) varies jointly as \(p\) and \(q .\) If \(p=4\) and \(q=5,\) then \(S=180\)

\(11-36\) Make a table of values and sketch the graph of the equation. Find the \(x\) - and \(y\) -intercepts. $$ y=9-x^{2} $$

Find an equation of the line that satisfies the given conditions. Through \((2,1)\) and \((1,6)\)

23-26 \(\mathbf{}\) Do the graphs intersect in the given viewing rectangle? If they do, how many points of intersection are there? $$ y=-3 x^{2}+6 x-\frac{1}{2}, y=\sqrt{7-\frac{7}{12} x^{2}} ; \quad[-4,4] \text { by }[-1,3] $$

Express the statement as an equation. Use the given information to find the constant of proportionality. \(W\) is inversely proportional to the square of \(r .\) If \(r=6,\) then \(W=10 .\)

\(11-36\) Make a table of values and sketch the graph of the equation. Find the \(x\) - and \(y\) -intercepts. $$ x y=2 $$

Find an equation of the line that satisfies the given conditions. Through \((-1,-2)\) and \((4,3)\)

23-26 \(\mathbf{}\) Do the graphs intersect in the given viewing rectangle? If they do, how many points of intersection are there? $$ y=\sqrt{49-x^{2}}, y=\frac{1}{5}(41-3 x) ; \quad[-8,8] \text { by }[-1,8] $$

Express the statement as an equation. Use the given information to find the constant of proportionality. \(t\) is jointly proportional to \(x\) and \(y\) and inversely proportional to \(r .\) If \(x=2, y=3,\) and \(r=12,\) then \(t=25\)

\(11-36\) Make a table of values and sketch the graph of the equation. Find the \(x\) - and \(y\) -intercepts. $$ x+y^{2}=4 $$

Find an equation of the line that satisfies the given conditions. Slope \(3 ; \quad y\) intercept \(-2\)

23-26 \(\mathbf{}\) Do the graphs intersect in the given viewing rectangle? If they do, how many points of intersection are there? $$ y=6-4 x-x^{2}, y=3 x+18 ;[-6,2] \text { by }[-5,20] $$