Chapter 2

We find the "steepness," or slope, of a line passing through two points by dividing the difference in the ________ \(-\) coordinates of these points by the difference in the _______ \(-\) coordinates. So the line passing through the points \((0,1)\) and \((2,5)\) has slope ________

If the quantities \(x\) and \(y\) are related by the equation \(y=3 x\) then we say that \(y\) is _____ _____ to \(x\) and the constant of _____ is 3.

The solutions of the equation \(x^{2}-2 x-3=0\) are the _________ intercepts of the graph of \(y=x^{2}-2 x-3\)

If the point \((2,3)\) is on the graph of an equation in \(x\) and \(y,\) then the equation is satisfied when we replace \(x\) by _____ and \(y\) by _____ Is the point \((2,3)\) on the graph of the equation \(2 y=x+1 ?\)

The point that is 3 units to the right of the y-axis and 5 units below the x-axis has coordinates (____,____).

A line has the equation \(y=3 x+2\) (a) This line has slope ______ (b) Any line parallel to this line has slope _____ (c) Any line perpendicular to this line has slope ______

If the quantities \(x\) and \(y\) are related by the equation \(y=\frac{3}{x},\) then we say that \(y\) is _____ _____ to \(x\) and the constant of _____ is 3.

The solutions of the inequality \(x^{2}-2 x-3>0\) are the \(x\) -coordinates of the points on the graph of \(y=x^{2}-2 x-3\) that lie ______the \(x\) -axis.

(a) To find the \(x\) -intercept(s) of the graph of an equation, we set _____ equal to 0 and solve for _____ So the \(x\) -intercept of \(2 y=x+1\) is _____. (b) To find the \(y\) -intercept(s) of the graph of an equation, we set _____ equal to 0 and solve for _____ So the \(y\) -intercept of \(2 y=x+1\) is _____.

If x is negative and y is positive, then the point (x, y) is in Quadrant ________.

The point-slope form of the equation of the line with slope 3 passing through the point \((1,2)\) is _______

The graph of the equation \((x-1)^{2}+(y-2)^{2}=9\) is a circle with center (_____,_____) and radius _____.

The distance between the points \((a, b)\) and \((c, d)\) is ________. So the distance between \((1,2)\) and \((7,10)\) is ________.

(a) The slope of a horizontal line is _______ The equation of the horizontal line passing through \((2,3)\) is (b) The slope of a vertical line is ________ The equation of the vertical line passing through \((2,3)\) is ________

If \(z\) is jointly proportional to \(x\) and \(y\) and if \(z\) is 10 when \(x\) is 4 and \(y\) is \(5,\) then \(x, y,\) and \(z\) are related by the equation \(z=\) _____.

(a) If a graph is symmetric with respect to the \(x\) -axis and \((a, b)\) is on the graph, then (_____,____) is also on the graph. (b) If a graph is symmetric with respect to the \(y\) -axis and \((a, b)\) is on the graph, then (_____,_____) is also on the graph. (c) If a graph is symmetric about the origin and \((a, b)\) is on the graph, then (_____,_____) is also on the graph.

The point midway between \((a, b)\) and \((c, d)\) is ________. So the point midway between \((1,2)\) and \((7,10)\) is ________.

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

Write an equation that expresses the statement. T varies directly as \(x\)

\(5-10\) Use a graphing calculator or computer to decide which viewing rectangle \((a)-(\text { d) produces the most appropriate graph }\) of the equation. $$ \begin{array}{l}{y=x^{4}+2} \\ {\text { (a) }[-2,2] \text { by }[-2,2]} \\\ {\text { (b) }[0,4] \text { by }[0,4]} \\ {\text { (c) }[-8,8] \text { by }[-4,40]} \\ {\text { (d) }[-40,40] \text { by }[-80,800]}\end{array} $$

\(5-10\) . Determine whether the given points are on the graph of the equation. $$ y=3 x-2 ; \quad(0,2),\left(\frac{1}{3}, 1\right),(1,1) $$

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

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

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

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

\(5-10\) . Determine whether the given points are on the graph of the equation. $$ y=\sqrt{x+1} ; \quad(1,0),(0,1),(3,2) $$

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

\(5-10\) Use a graphing calculator or computer to decide which viewing rectangle \((a)-(\text { d) produces the most appropriate graph }\) of the equation. $$ \begin{array}{l}{y=100-x^{2}} \\ {\text { (a) }[-4,4] \text { by }[-4,4]} \\\ {\text { (b) }[-10,10] \text { by }[-10,10]} \\ {\text { (c) }[-15,15] \text { by }[-30,110]} \\ {\text { (d) }[-4,4] \text { by }[-30,110]}\end{array} $$

Write an equation that expresses the statement. \(v\) is inversely proportional to \(z\)

\(5-10\) . Determine whether the given points are on the graph of the equation. $$ x-2 y-1=0 ; \quad(0,0),(1,0),(-1,-1) $$

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

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

\(5-10\) Use a graphing calculator or computer to decide which viewing rectangle \((a)-(\text { d) produces the most appropriate graph }\) of the equation. $$ \begin{array}{l}{y=2 x^{2}-1000} \\ {\text { (a) }[-10,10] \text { by }[-10,10]} \\ {\text { (b) }[-10,10] \text { by }[-100,100]} \\ {\text { (c) }[-10,10] \text { by }[-1000,1000]} \\ {\text { (d) }[-25,25] \text { by }[-1200,200]}\end{array} $$

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

\(5-10\) . Determine whether the given points are on the graph of the equation. $$ y\left(x^{2}+1\right)=1 ; \quad(1,1),\left(1, \frac{1}{2}\right),\left(-1, \frac{1}{2}\right) $$

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

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

\(5-10\) Use a graphing calculator or computer to decide which viewing rectangle \((a)-(\text { d) produces the most appropriate graph }\) of the equation. $$ \begin{array}{l}{y=10+25 x-x^{3}} \\ {\text { (a) }[-4,4] \text { by }[-4,4]} \\\ {\text { (b) }[-10,10] \text { by }[-10,10]} \\ {\text { (c) }[-20,20] \text { by }[-100,100]} \\ {\text { (d) }[-100,100] \text { by }[-200,200]}\end{array} $$

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

\(5-10\) . Determine whether the given points are on the graph of the equation. $$ x^{2}+x y+y^{2}=4 ; \quad(0,-2),(1,-2),(2,-2) $$

Sketch the region given by the set. \(\\{(x, y) | x=3\\}\)

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

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

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

\(5-10\) . Determine whether the given points are on the graph of the equation. $$ x^{2}+y^{2}=1 ; \quad(0,1),\left(\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}\right),\left(\frac{\sqrt{3}}{2}, \frac{1}{2}\right) $$

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

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

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

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

Sketch the region given by the set. \(\\{(x, y) | 1< x< 2\\}\)