Algebra Chapter 3

Graphing Linear Equations and Function

3.1 Plot Points in a Coordinate Plane

Quadrants: ______

Example 1: Give the coordinates of the point.

a.A
b.B
c.C
d.D
e.E /

Example 2: Plot the point in a coordinate plane. Describe the location of the point.

a.A(1, –3)
b.B(–2, –2)
c.C(–3, 0)
d.D(3, 5)
e.E(0, –4)
f.F(4, –2) /

Example 3: Graph the function y =x + 2 with domain –6, –4, –2, 0, and 2. Then identify the range of the function.

x / y=x + 2 /
–6
–4
–2
0
2

Example 4: The table shows attendance at a school carnival before and after the school added game booths in 2002.

Years, x, before or since 2002 / -2 / -1 / 0 / 1
Attendance, y (hundreds) / 2.6 / 2.2 / 3.1 / 3.5
  1. Explain how you know the table represents a function.
  1. Graph the function.
  1. Describe any trends.

3.2 Graph Linear Equations

A solution of an equation in two variables: ______

______

Thegraph of an equation in two variables:______

______

A linear equation: ______

The standard form of a linear equation:______

______

Linear function: ______

Example 1: Tell whether the ordered pair is a solution of the equation.

1.–2x +3y = –7; (2, –1)2. x =–3; (0, –3)

3. x –y = 4; (9, 2)

Example 2: Graph the equation 3y = x –3.

x
y
/

Example 3: Graph y = -3 and x = 2

Example 4: Graph the function y =–x + 3 with domain –1  x  4. Then identify the range of the function.

x / –1 / 0 / 1 / 2 / 3 / 4
y
/

Example 5: The number of pages a student types is given by p = 4t where t is the time (in hours) spent typing. The student plans to type for at most 2.5 hours. Graph the function and identify its domain and range.

3.3 Graph Using Intercepts

x-intercept: ______

y-intercept: ______

Example 1: Find the x-intercept and the y-intercept of the graph of 7x – 3y = 21.


Example 2: Identify the x-intercept and y-intercept of the graph.

Example 3: Graph 3x + 2y = 6. Label the points where the line crosses the axis.

3.4 Find Slope and Rate of Change

Slope: ______

______

Rate of change: ______

Example1: Find the slope of the line shown.



Example 2: Find the slope of the line shown.

The line falls from left to right. The slope is negative.


Example 3: Find the slope of the line shown.

Example 4: Find the slope of the line through (-2, -1) and (4 -1).

Example 5: The table shows the amount of water evaporating from a swimming pool on a hot day. Find the rate of change in gallons with respect to time. Time (hours)

Time (hours) / 2 / 3 / 12
Gallons evaporated / 4.5 / 13.5 / 27

Example 6: The graph shows the number of computer games sold day 1, day 4, day 7, and day 9 of a sale. Describe the rates of change in sales with respect to time.

3.5 Graph Using Slope-Intercept Form

Slope-intercept form: ______

______

Parallel: ______

Example 1: Identify the slope and y-intercept of the line with the given equation.

a. b. – 2x + 3y = 9 c. y = – 3x + 7

d.15x – 5y = 10e. – x – 6y = 18

Example 2: Graph the equations: a. 4x + y = 3 b. y = – 1 c. y = – x

Example 3: Determine which of the lines are parallel: line a through (–3, 1) and (–6, 7); line b through

(–7, –5) and (1, 11); line c through (2, 5) and (4, 9).

Example 4: You can use a laser or inkjet printer to print an 18 page report. The laser printer prints 6 pages per minute and the inkjet printer prints 4.5 pages per minute. The models give the number of pages p left to print after t minutes.

Laser: p = -6t + 18Inkjet: p = -4.5t + 18

  1. Graph both models in the same coordinate plane.
  2. How many minutes do you save by using the laser printer?
/

Example 5: A violin teacher charges a one-time sheet music fee of $20 for adults and no fee for children. The charge per hour is $20 for both children and adults. The cost C for children for n lessons is given by C = 20n and for adults by C = 20n + 20.

  1. Graph both equations in the same coordinate plane.
  2. Based on the graphs, what is the difference in the costs?
/

3.6 Model Direct Variation

Direct variation: ______

Constant of variation: ______

Example 1: Tell whether the equation represents direct variation. If so, identify the constant of variation.

a.6x –3y = 12b. –5x +2y = 0c. 3x + 5y = 0

Example 2: The graph of a direct variation equation is shown.

aWrite the direct variation equation.
bFind the value of y when x = 12. /

Example 3: The table shows the cost C of purchasing tickets for a rock concert.

  1. Explain why C varies directlywith t
  2. Write a direct variation equationthat relates t and C.

Number of tickets,t / Cost, C
2 / $36
3 / $54
5 / $90

Example 4: An object that weighs 100 pounds on Earth would weigh just 6 pounds on Pluto. Assume that the weight P on Pluto varies directly with weight E on Earth.

  1. Write a direct variation equation that relates P and E.
  2. What would a boulder weighing 750 pounds on Earth weigh on Pluto?

3.7 Graph Linear Functions

Function notation: ______

A family of functions: ______

Parent linear function: ______

Example 1: Evaluate the function for the given value of x.

1.f (x) = 0.3x – 1.2; 72. g(x) = x + ; 4

Example 2: For the function f (x) = –3x + 2, find the value of x so that f (x) = –13.

Example 3:Graph the functions. Compare the graph with the graph of f (x) = x.

m(x) = xn(x) = x – 2