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 / Balance1 / $128
2 / $142
3 / $156
4 / $170
5 / $184
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 the end / · 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
5. 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 LinesPerpendicular 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 FormWritten 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)
2. 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).
3. 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.
4. 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?
5. 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?
6. 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 DETERMINE LINE 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.
Is (3, 4) a solution? Explain. Is (-1, -3) a solution? Explain.
7. Which of the following linear inequalities is shown graphed below?
(1) (3)
(2) (4)
WRITING AND GRAPHING LINEAR EQUATIONS/INEQUALITIES (Day 6)
Write an equation/inequality for each below and state a possible solution for each graph.
· Recall: Inequality Equations have ______(determine using test point)
1. 2.
3. 4.
Graph the following: When appropriate label the solution area with a “S”
5. 6.
7. 8. Write and appropriate equation
or inequality of the graph below.
Is (4, 4) a solution? Explain.
LINEAR FUNCTION APPLICATION PROBLEMS (Day 7)
1. Mirka is baking apple pies to sell. She has to purchase a glass pie plate for $10 and apples cost $5 per pound.
a) Write a function that represents Mirka’s cost, C, if she buys a pounds of apples.
b) What are the domain and range of the function in this situation?
c) Using the grid below, sketch a graph of the function over the domain you chose.
d) How many pounds of apples did Mirka buy if she spent $37.50? Justify your answer.
2. The population of deer in a park is growing over the years. The table below gives the population found in a survey by local wildlife officials.
Year / 2000 / 2003 / 2006 / 2009Deer Population / 168 / 216 / 264 / 312
(a) Find the average rate that the deer population is changing over each time interval below:
From 2000 to 2003 From 2006 to 2009
(b) Why does this calculation indicate a linear relationship?
(c) If T stands for the number of years since 2000, write an equation for the deer population, p, as a function of T.
(d) What does your model predict the deer population to be in the year 2014?
(e) How many years will it take for the deer population to reach 500? Round to the nearest year.
Linear Inequality Application Problems (Day 8)
1. Olivia is going to a Halloween party and needs to bring an appetizer. She only has $50.00 to spend. She decides to make a cheese and grape tray. One pound of grapes cost $3.00 and cheese costs $5.00 per pound.
a) Write an inequality to represent the amount of cheese and grapes 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 grapes she could buy.
2) Sarah is selling bracelets and earrings to make money for a summer vacation. The bracelets cost $2 and the earrings cost $3. She needs to make more than $600 to pay for her vacation.
a) Write a function to represent the number of bracelets and earrings Sarah sells in relation to the amount of money she needs to make.
b) Using the grid below, sketch a graph of the function and state one possible combination of bracelets and earrings sold.
c) Explain what the point (24,184) represents in this model. Would Sarah be able to pay for her vacation? Explain your answer.
16