GRAPHING LINEAR FUNCTIONS – ALGEBRA – UNIT 4

SLOPE/RATE OF CHANGE(Day 1)

There are FOUR types of slope.

SLOPE/RATE OF CHANGE

Find the slope of the following using the Slope Formula:

1.(0, -2) & (2, 4)2.(0, 3) & (4, 3)3.(-2, 2) & (4, -1)

Find the slope of the following, using the method:

4. (2, 3) & (-4, -5) 5. (-5, 2) & (4, -3)

Week / Balance
1 / $128
2 / $142
3 / $156
4 / $170
5 / $148

6. Find the average rate of change of the function shown to the right that represents the amount of money in a savings account Lender’s Bank?

7.Given the function find:

a)f(2) b) f(10)

c) the rate of change in the interval [2,10]

8.Given the function graphed below. Find the average rate of change in the interval [-3, 0].

9.Given the table of values below for a function, find the average rate of change of this function from t = -3 to t = 5.

t / f(t)
-4 / 6
-3 / 1
-2 / -2
-1 / -3
0 / -2
1 / 1
2 / 6
3 / 13
4 / 22
5 / 33

GRAPHING LINEAR FUNCTIONS (Day 2)

TYPES OF LINES/KEY FEATURES

HORIZONTAL / VERTICAL / DIAGONAL (SLANTED)

HOW TO GRAPH LINEAR FUNCTIONS

OPTION 1: No Graphing Calculator / OPTION 2: Graphing Calculator
  • Identify type of Line to be graphed
Horizontal -- HOY (y = #)
Vertical -- VUX (x = #)
Diagonal -- (y = mx + b)
Make sure all equations are in y = mx + b before completing the following steps.
  • Plot y-intercept (b#) on graph for starting point
  • Create multiple points in both directions using the slope (m #) by doing
  • Connect all points and put arrows on theend
/
  • Put equation into graphing calculator.
  • Write down a table of values from calculator
  • Plot points and connect with a line that ends with arrows.
CALCULATOR STEPS:
  • Press y = button to input equation
  • Input equation into y1
  • Press 2nd Graph to get a table of values

  1. Graph a line that has a slope of –1and goes
    through the point (-1, 4).

2.Graph a line that goes through the point (3, 1) and
has a slope of .

3. Graph:4. Graph

  1. Which is the equation of a line with a slope of -2 that passes through the point (-2, 0)?

(1) (2) (3) (4)

6. Write an equation of a line that is:

(a)Parallel to the x-axis and 2 units above it.

(b) Parallel to the y-axis and 2 units to the left of it.

(c) Has undefined slope and passes through the point (3, -4).

(d) Has a slope of 0 and passes through the point (-7, -8).

Write an equation for each of the graphed functions below using function notation.

7.8.9.

Parallel and Perpendicular Lines (Day 3)

Parallel Lines /
Perpendicular Lines /

1.Write the equation of a line that is parallel to 3y – 2x = 6 and has a y-intercept of -4.

2.Write the equation of a line that is perpendicular to y + 5 = -3x and goes through the point (0, 7).

3.Graph a line perpendicular to the given line that goes through the point (-2, 2).

What is the equation of this line?

4.Graph a line that is parallel to the given line and has y-intercept of -1.

What is the equation of this line?

5.Write an equation of a line that is:

a) Parallel to the x-axis and 3 units below it.

b) Perpendicular to the y-axis and goes through the point (-3, 7).

c) Has undefined slope and passes through the point (5, -6).

d) Has a slope of 0 and passes through the point (4, 1).

e)Parallel to the y-axis and 5 units to the left of it.

f) Perpendicular to the x-axis and goes through the point (0, 9).

6.Which equation represents a line perpendicular to 3y – 1 = 2x?

(1) y = -x + 6(3) y = x -

(2) y = x + 3(4) y = -x -

7.What is the equation of the line that has a y-intercept of –2 and is parallel to the line whose equation is -2y = 4x + 8?

(1) y = x – 2 (3) y = 2x + 2

(2) y = -2x – 2 (4) y = -x – 2

WRITING LINEAR FUNCTIONS (Day 4)

Slope – Intercept Form / Standard Form

Written using Function Notation: / Written using Function Notation:
  1. Alex makes ceramic bowls to sell at a monthly craft fair in a nearby city. Every month, she spends $50 on materials for the bowls from a local art store. At the fair, she sells each completed bowl for a total of $25 including tax. Which equation expresses Alex’s profit as a function of the number of bowls that she sells in one month?

(1)(3)

(2)(4)

  1. Samuel’s Car Service will charge a flat travel fee of $4.75 for anyone making a trip. They charge an additional set rate of $1.50 per mile that is traveled. Write an equation that represents the charges as a function C(m).
  1. Veronica earned $150 at work this past week in her paycheck. She wants to buy some necklaces which cost $6 each. She writes a function to model the amount of money she will have left from her paycheck after purchasing a certain number of necklaces. She writes the function, . Determine what x and f(x) represent in the function.
  1. Jonathan has been on a diet since January 2013. So far, he has been losing weight at a steady rate. Based on monthly weigh-ins, his weight, w, can be modeled by the function , where m is the number of months after January 2013.

a) How much did Jonathan weigh at the start of the diet?

b) How much weight has Jonathan been losing each month?

c)How many months did it take Jonathan to lose 45 pounds?

  1. The cost of operating Jelly’s Doughnuts is $1600 per week plus $.10 to make each doughnut.

a)Write a function C(d), to model the company’s weekly cost for producing d doughnuts.

b)What is the total weekly cost if the company produces 4,000 doughnuts?

c)Jelly’s Doughnuts makes a gross profit of $.60 for each doughnut they sell. If they sold all 4000 doughnuts they made, would they make money or lose money for the week? How much?

  1. Andy graphed his wages and tips after several weeks of driving deliveries. Given the graph, write his earnings as a function of the number of deliveries that he made.

GRAPHING LINEAR INEQUALITIES (Day 5)

STEPS:

  1. Determine type of line to be graphed:
  2. Identify Slope and y-interpret
  3. Plot points (do not connect yet), then DETERMINELINE TYPE

If the equation has a ____or ____ sign then you connect the points with a: ______

If the equation has a _____ or______sign then you connect the points with: ______

Determine Shading by Picking a test point: (mark test point with an x on the graph)

  • Shade where test point is ______!!

Graph the following, label the solution area with a ‘S’, and identify a point in the solution.

1. y < 3 2.x 2

3. 4.

5. 6. x – 3y > -6

  1. 8.

9.10.

WRITING AND GRAPHING LINEAR EQUATIONS/INEQUALITIES (Day 6)

Write an equation/inequality for each below and state a possible solution for each graph.

1.2.

3.4.

Graph the following: When appropriate label the solution area with a “S”

7.8.

9.10.

11.12.

LINEAR FUNCTION APPLICATION PROBLEMS (Day 7)

x / f(x)
3
625
7
2575
  1. Sam’s profit after a year of selling custom bicycles that he has created can be represented by the function

Complete the accompanying table that represents his profits

from the past year.

In which month of the year did he begin to make a profit?

Explain your answer.

  1. Tina is looking to join a monthly coffee delivery club for the 10 months that she works. She found a coffee shop that offers this service for $40 startup fee and $8 per month.

Write an equation that represents the cost as a function C(m).

What is the domain of the function for this situation?

Using the grid below, sketch a graph of the function over the domain you chose.

Linear Inequality Application Problems (Day 8)

1.Olivia is going to a July 4th party and needs to bring an appetizer. She only has $50 to spend on the appetizer. She decides to take a cheese and cracker tray. One package of crackers cost $3 and the cheese costs $5 per pound.

a)Write an inequality to represent the amount of cheese and crackers Olivia can take in relation to the amount of money she has to spend.

b)Using the grid below, sketch a graph of the inequality and state one possible amount of cheese and crackers she could buy.

  1. Shannon makes a weekly allowance of $25. She also makes $9.50 an hour at her job. Because of her age, Shannon can work no morethan 20 hours a week.
  1. Write a function for the amount of money she makes each week based on the amount of hours, h, she works.
  1. What is the domain of the function for this situation?
  1. Using the grid below, sketch a graph of the function over the domain you chose.

1