Intermediate Algebra

Lynn Marecek

Chapter 3

Graphs and Functions - all with Video Answers

Educators

Section 1

Graph Linear Equations in Two Variables

Problem 1

In the following exercises, plot each point in a rectangular coordinate system and identify the quadrant in which the point is located.
(a) $(-4,2)$
(b) $(-1,-2)$
(c) $(3,-5)$
(d) $(-3,0)$
(e) $\left(\frac{5}{3}, 2\right)$

Karla Conrey

Karla Conrey

Numerade Educator

Problem 2

In the following exercises, plot each point in a rectangular coordinate system and identify the quadrant in which the point is located.

(a) $(-2,-3)$
(b) $(3,-3)$
(c) $(-4,1)$
(d) $(4,-1)$
(e) $\left(\frac{3}{2}, 1\right)$

Karla Conrey

Numerade Educator

Problem 3

In the following exercises, plot each point in a rectangular coordinate system and identify the quadrant in which the point is located.

(a) $(3,-1)$
(b) $(-3,1)$
(c) $(-2,0)$
(d) $(-4,-3)$
(e) $\left(1, \frac{14}{5}\right)$

Karla Conrey

Numerade Educator

Problem 4

In the following exercises, plot each point in a rectangular coordinate system and identify the quadrant in which the point is located.

(a) $(-1,1)$
(b) $(-2,-1)$
(c) $(2,0)$
(d) $(1,-4)$
(e) $\left(3, \frac{7}{2}\right)$

Karla Conrey

Numerade Educator

Problem 5

In the following exercises, for each ordered pair, decide
(a) is the ordered pair a solution to the equation? (b) is the point on the line?
Graph can't copy
$y=x+2$;
A: $(0,2) ;$
B: $(1,2) ;$
C: $(-1,1)$;
D: $(-3,-1)$.

Karla Conrey

Numerade Educator

Problem 6

In the following exercises, for each ordered pair, decide
(a) is the ordered pair a solution to the equation? (b) is the point on the line?
Graph can't copy

$y=x-4$;
A: $(0,-4)$;
B: $(3,-1)$;
C: $(2,2)$;
D: $(1,-5)$.

Karla Conrey

Numerade Educator

Problem 7

In the following exercises, for each ordered pair, decide
(a) is the ordered pair a solution to the equation? (b) is the point on the line?
Graph can't copy
$y=\frac{1}{2} x-3$;
A: $(0,-3)$;
B: $(2,-2)$;
C: $(-2,-4)$;
D: $(4,1)$

Karla Conrey

Numerade Educator

Problem 8

In the following exercises, for each ordered pair, decide
(a) is the ordered pair a solution to the equation? (b) is the point on the line?
Graph can't copy

$y=\frac{1}{3} x+2$;
A: $(0,2)$;
B: $(3,3)$;
C: $(-3,2)$;
D: $(-6,0)$.

Karla Conrey

Numerade Educator

Problem 9

In the following exercises, graph by plotting points.
$y=x+2$

Emily Schilz

Numerade Educator

Problem 10

In the following exercises, graph by plotting points.
$y=x-3$

Emily Schilz

Numerade Educator

Problem 11

In the following exercises, graph by plotting points.
$y=3 x-1$

Emily Schilz

Numerade Educator

Problem 12

In the following exercises, graph by plotting points.
$y=-2 x+2$

Emily Schilz

Numerade Educator

Problem 13

In the following exercises, graph by plotting points.
$y=-x-3$

Ashton Collins

Numerade Educator

Problem 14

In the following exercises, graph by plotting points.
$y=-x-2$

Emily Schilz

Numerade Educator

Problem 15

In the following exercises, graph by plotting points.
$y=2 x$

Emily Schilz

Numerade Educator

Problem 16

In the following exercises, graph by plotting points.
$y=-2 x$

Emily Schilz

Numerade Educator

Problem 17

In the following exercises, graph by plotting points.
$y=\frac{1}{2} x+2$

Emily Schilz

Numerade Educator

Problem 18

In the following exercises, graph by plotting points.
$y=\frac{1}{3} x-1$

Emily Schilz

Numerade Educator

Problem 19

In the following exercises, graph by plotting points.
$y=\frac{4}{3} x-5$

Emily Schilz

Numerade Educator

Problem 20

In the following exercises, graph by plotting points.
$y=\frac{3}{2} x-3$

Emily Schilz

Numerade Educator

Problem 21

In the following exercises, graph by plotting points.
$y=-\frac{2}{5} x+1$

Emily Schilz

Numerade Educator

Problem 22

In the following exercises, graph by plotting points.
$y=-\frac{4}{5} x-1$

Emily Schilz

Numerade Educator

Problem 23

In the following exercises, graph by plotting points.
$y=-\frac{3}{2} x+2$

Emily Schilz

Numerade Educator

Problem 24

In the following exercises, graph by plotting points.
$y=-\frac{5}{3} x+4$

Emily Schilz

Numerade Educator

Problem 25

In the following exercises, graph each equation.
(a) $x=4$
(b) $y=3$

Jessica Kluck

Numerade Educator

Problem 26

In the following exercises, graph each equation.
(a) $x=3$
(b) $y=1$

Jessica Kluck

Numerade Educator

Problem 27

In the following exercises, graph each equation.

(a) $x=-2$
(b) $y=-5$

Jessica Kluck

Numerade Educator

Problem 28

In the following exercises, graph each equation.

(a) $x=-5$
(b) $y=-2$

Jessica Kluck

Numerade Educator

Problem 29

In the following exercises, graph each pair of equations in the same rectangular coordinate system.
$y=2 x$ and $y=2$

Daniel Carr

Numerade Educator

Problem 30

In the following exercises, graph each pair of equations in the same rectangular coordinate system.
$y=5 x$ and $y=5$

Alison Rodriguez

Alison Rodriguez

Numerade Educator

Problem 31

In the following exercises, graph each pair of equations in the same rectangular coordinate system.
$y=-\frac{1}{2} x$ and $y=-\frac{1}{2}$

Emily Schilz

Numerade Educator

Problem 32

In the following exercises, graph each pair of equations in the same rectangular coordinate system.
$y=-\frac{1}{3} x$ and $y=-\frac{1}{3}$

Karla Conrey

Numerade Educator

Problem 33

In the following exercises, find the $x$ - and $y$-intercepts on each graph.
Graph can't copy

Ashton Collins

Numerade Educator

Problem 34

In the following exercises, find the $x$ - and $y$-intercepts on each graph.
Graph can't copy

Ashton Collins

Numerade Educator

Problem 35

In the following exercises, find the $x$ - and $y$-intercepts on each graph.
Graph can't copy

Ashton Collins

Numerade Educator

Problem 36

In the following exercises, find the $x$ - and $y$-intercepts on each graph.
Graph can't copy

Ashton Collins

Numerade Educator

Problem 37

In the following exercises, find the intercepts for each equation.
$x-y=5$

Jessica Kluck

Numerade Educator

Problem 38

In the following exercises, find the intercepts for each equation.
$x-y=-4$

Jessica Kluck

Numerade Educator

Problem 39

In the following exercises, find the intercepts for each equation.
$3 x+y=6$

Jessica Kluck

Numerade Educator

Problem 40

In the following exercises, find the intercepts for each equation.
$x-2 y=8$

Jessica Kluck

Numerade Educator

Problem 41

In the following exercises, find the intercepts for each equation.
$4 x-y=8$

Jessica Kluck

Numerade Educator

Problem 42

In the following exercises, find the intercepts for each equation.
$5 x-y=5$

Jessica Kluck

Numerade Educator

Problem 43

In the following exercises, find the intercepts for each equation.
$2 x+5 y=10$

Jessica Kluck

Numerade Educator

Problem 44

In the following exercises, find the intercepts for each equation.
$3 x-2 y=12$

Jessica Kluck

Numerade Educator

Problem 45

In the following exercises, graph using the intercepts.
$-x+4 y=8$

Jessica Kluck

Numerade Educator

Problem 46

In the following exercises, graph using the intercepts.
$x+2 y=4$

Cory Kuzinski

Numerade Educator

Problem 47

In the following exercises, graph using the intercepts.
$x+y=-3$

Cory Kuzinski

Numerade Educator

Problem 48

In the following exercises, graph using the intercepts.
$x-y=-4$

Jessica Kluck

Numerade Educator

Problem 49

In the following exercises, graph using the intercepts.
$4 x+y=4$

Karuna Ramroop

Numerade Educator

Problem 50

In the following exercises, graph using the intercepts.
$3 x+y=3$

Ashton Collins

Numerade Educator

Problem 51

In the following exercises, graph using the intercepts.
$3 x-y=-6$

Cory Kuzinski

Numerade Educator

Problem 52

In the following exercises, graph using the intercepts.
$2 x-y=-8$

Jessica Kluck

Numerade Educator

Problem 53

In the following exercises, graph using the intercepts.
$2 x+4 y=12$

James Kiss

Numerade Educator

Problem 54

In the following exercises, graph using the intercepts.
$3 x-2 y=6$

Cory Kuzinski

Numerade Educator

Problem 55

In the following exercises, graph using the intercepts.
$2 x-5 y=-20$

Karla Conrey

Numerade Educator

Problem 56

In the following exercises, graph using the intercepts.
$3 x-4 y=-12$

James Kiss

Numerade Educator

Problem 57

In the following exercises, graph using the intercepts.
$y=-2 x$

Cory Kuzinski

Numerade Educator

Problem 58

In the following exercises, graph using the intercepts.
$y=5 x$

Jessica Kluck

Numerade Educator

Problem 59

In the following exercises, graph using the intercepts.
$y=x$

Jessica Kluck

Numerade Educator

Problem 60

In the following exercises, graph using the intercepts.
$y=-x$

Cory Kuzinski

Numerade Educator

Problem 61

In the following exercises, graph each equation.
$y=\frac{3}{2} x$

Jessica Kluck

Numerade Educator

Problem 62

In the following exercises, graph each equation.
$y=-\frac{2}{3} x$

Jessica Kluck

Numerade Educator

Problem 63

In the following exercises, graph each equation.
$y=-\frac{1}{2} x+3$

Melissa Barry

Numerade Educator

Problem 64

In the following exercises, graph each equation.
$y=\frac{1}{4} x-2$

Hong Joo Ryoo

Numerade Educator

Problem 65

In the following exercises, graph each equation.
$4 x+y=2$

Karla Conrey

Numerade Educator

Problem 66

In the following exercises, graph each equation.
$5 x+2 y=10$

Karla Conrey

Numerade Educator

Problem 67

In the following exercises, graph each equation.
$y=-1$

Karla Conrey

Numerade Educator

Problem 68

In the following exercises, graph each equation.
$x=3$

Karla Conrey

Numerade Educator

Problem 69

Explain how you would choose three $x$-values to make a table to graph the line $y=\frac{1}{5} x-2$.

Emily Schilz

Numerade Educator

Problem 70

What is the difference between the equations of a vertical and a horizontal line?

Emily Schilz

Numerade Educator

Problem 71

Do you prefer to use the method of plotting points or the method using the intercepts to graph the equation $4 x+y=-4$ ? Why?

Karla Conrey

Numerade Educator

Problem 72

Do you prefer to use the method of plotting points or the method using the intercepts to graph the equation $y=\frac{2}{3} x-2$ ? Why?

Karla Conrey

Numerade Educator