Chapter 3

Algebra for College Students · 201 exercises

Problem 32

Graph each linear equation. Plot four points for each line. $$x=-3$$

4 step solution

Problem 32

Find the slope of the line that contains each of the following pairs of points. \((1988,306),(1990,315)\)

4 step solution

Problem 33

Determine which of the ordered pairs \((1,3),(-2,5)\) \((-6,-4),\) and \((7,-8)\) satisfy each compound or absolute value inequality. $$y>4 \text { or } x<1$$

3 step solution

Problem 33

Graph each linear equation. Plot four points for each line. $$y=\frac{1}{2} x-1$$

5 step solution

Problem 33

Find the slope of the line that contains each of the following pairs of points. \((4,7),(-12,7)\)

5 step solution

Problem 34

Determine which of the ordered pairs \((1,3),(-2,5)\) \((-6,-4),\) and \((7,-8)\) satisfy each compound or absolute value inequality. $$y<2 \text { or } x<0$$

4 step solution

Problem 34

Graph each linear equation. Plot four points for each line. $$y=\frac{1}{3} x-2$$

8 step solution

Problem 34

Find the slope of the line that contains each of the following pairs of points. \((5,-3),(9,-3)\)

4 step solution

Problem 35

Determine which of the ordered pairs \((1,3),(-2,5)\) \((-6,-4),\) and \((7,-8)\) satisfy each compound or absolute value inequality. \(y>4\) and \(x<1\)

6 step solution

Problem 35

Graph each linear equation. Plot four points for each line. $$y+3=0$$

5 step solution

Problem 35

Find the slope of the line that contains each of the following pairs of points. \((2,6),(2,-6)\)

5 step solution

Problem 36

Determine which of the ordered pairs \((1,3),(-2,5)\) \((-6,-4),\) and \((7,-8)\) satisfy each compound or absolute value inequality. \(y<2\) and \(x<0\)

5 step solution

Problem 36

Graph each linear equation. Plot four points for each line. $$y+4=0$$

5 step solution

Problem 37

Determine which of the ordered pairs \((1,3),(-2,5)\) \((-6,-4),\) and \((7,-8)\) satisfy each compound or absolute value inequality. $$y>5 x \text { and } y<-x$$

5 step solution

Problem 37

Graph each linear equation. Plot four points for each line. $$x-4=0$$

5 step solution

Problem 37

Find the slope of the line that contains each of the following pairs of points. $$(24.3,11.9),(3.57,8.4)$$

7 step solution

Problem 38

Determine which of the ordered pairs \((1,3),(-2,5)\) \((-6,-4),\) and \((7,-8)\) satisfy each compound or absolute value inequality. $$y>5 x \text { and } y>-x$$

5 step solution

Problem 38

Graph each linear equation. Plot four points for each line. $$x+5=0$$

4 step solution

Problem 38

Find the slope of the line that contains each of the following pairs of points. $$(-2.7,19.3),(5.46,-3.28)$$

7 step solution

Problem 39

Determine which of the ordered pairs \((1,3),(-2,5)\) \((-6,-4),\) and \((7,-8)\) satisfy each compound or absolute value inequality. $$y>-x+1 \text { or } y>4 x$$

4 step solution

Problem 39

Graph each pair of lines in the same coordinate system using the slope and y-intercept. $$\begin{aligned}&y=x+3\\\&y=x+2\end{aligned}$$

4 step solution

Problem 39

Graph each linear equation. Plot four points for each line. $$y=\frac{1}{2} x$$

5 step solution

Problem 40

Determine which of the ordered pairs \((1,3),(-2,5)\) \((-6,-4),\) and \((7,-8)\) satisfy each compound or absolute value inequality. $$y>-x+1 \text { or } y<4 x$$

6 step solution

Problem 40

Graph each pair of lines in the same coordinate system using the slope and y-intercept. $$\begin{aligned}&y=-x+2\\\&y=-x-2\end{aligned}$$

8 step solution

Problem 40

Graph each linear equation. Plot four points for each line. $$y=-\frac{2}{3} x$$

5 step solution

Problem 41

Determine which of the ordered pairs \((1,3),(-2,5)\) \((-6,-4),\) and \((7,-8)\) satisfy each compound or absolute value inequality. $$|x+y|<3$$

5 step solution

Problem 41

Graph each pair of lines in the same coordinate system using the slope and y-intercept. $$ \begin{array}{l} y=3 x+1 \\ y=-\frac{1}{3} x+1 \end{array} $$

9 step solution

Problem 41

Graph each linear equation. Plot four points for each line. $$3 x+y=5$$

6 step solution

Problem 42

Determine which of the ordered pairs \((1,3),(-2,5)\) \((-6,-4),\) and \((7,-8)\) satisfy each compound or absolute value inequality. $$|x-y|>2$$

5 step solution

Problem 42

Graph each pair of lines in the same coordinate system using the slope and y-intercept. $$ \begin{aligned} &y=2 x+3\\\ &y=-\frac{1}{2} x+3 \end{aligned} $$

9 step solution

Problem 42

Graph each linear equation. Plot four points for each line. $$x+2 y=4$$

5 step solution

Problem 43

Graph each pair of lines in the same coordinate system using the slope and y-intercept. $$ \begin{aligned} &y=\frac{2}{3} x-1\\\ &y=\frac{2}{3} x+1 \end{aligned} $$

8 step solution

Problem 43

Graph each linear equation. Plot four points for each line. $$6 x+3 y=0$$

5 step solution

Problem 44

Graph each pair of lines in the same coordinate system using the slope and y-intercept. $$ \begin{aligned} &y=-2 x+4\\\ &y=-2 x+2 \end{aligned} $$

9 step solution

Problem 44

Graph each linear equation. Plot four points for each line. $$2 x+4 y=0$$

5 step solution

Problem 45

Graph each pair of lines in the same coordinate system using the slope and y-intercept. $$ \begin{aligned} &y=\frac{3}{4} x+3\\\ &y=-\frac{4}{3} x+1 \end{aligned} $$

9 step solution

Problem 45

Graph each linear equation. Plot four points for each line. $$y=2 x-20$$

5 step solution

Problem 46

Graph each pair of lines in the same coordinate system using the slope and y-intercept. $$ \begin{aligned} &y=\frac{2}{3} x+1\\\ &y=-\frac{3}{2} x+3 \end{aligned} $$

5 step solution

Problem 46

Graph each linear equation. Plot four points for each line. $$y=40-2 x$$

5 step solution

Problem 47

Find the \(x\) - and \(y\) -intercepts for each line and use them to graph the line. $$4 x-3 y=12$$

4 step solution

Problem 47

In each case find the slope of line I and graph both lines that are mentioned. Line \(l\) is perpendicular to a line with slope \(\frac{4}{5}\). Both lines contain the origin.

4 step solution

Problem 48

Find the \(x\) - and \(y\) -intercepts for each line and use them to graph the line. $$2 x+5 y=20$$

3 step solution

Problem 49

Find the \(x\) - and \(y\) -intercepts for each line and use them to graph the line. $$x-y+5=0$$

4 step solution

Problem 50

Find the \(x\) - and \(y\) -intercepts for each line and use them to graph the line. $$x+y+7=0$$

4 step solution

Problem 51

Find the \(x\) - and \(y\) -intercepts for each line and use them to graph the line. $$2 x+3 y=5$$

4 step solution

Problem 51

Determine whether the lines \(l_{1}\) and \(l_{2}\) are parallel, perpendicular, or neither. \(l_{1}\) goes through \((1,2)\) and \((4,8), l_{2}\) goes through \((0,3)\) and \((2,2)\)

3 step solution

Problem 52

Find the \(x\) - and \(y\) -intercepts for each line and use them to graph the line. $$3 x-4 y=7$$

3 step solution

Problem 52

Determine whether the lines \(l_{1}\) and \(l_{2}\) are parallel, perpendicular, or neither. \(I_{1}\) goes through \((-2,5)\) and \((3,7), l_{2}\) goes through \((8,4)\) and \((13,6)\)

3 step solution

Problem 53

Find the \(x\) - and \(y\) -intercepts for each line and use them to graph the line. $$2 x-3 y=60$$

5 step solution

Problem 53

Determine whether the lines \(l_{1}\) and \(l_{2}\) are parallel, perpendicular, or neither. \(l_{\mathrm{I}}\) goes through \((0,4)\) and \((-1,6), l_{2}\) goes through \((7,7)\) and \((8,9)\)

3 step solution

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