ALGEBRA ITips, Tricks

and TI-Calculator

By: Alycia DiPinto

Algebra I

• Pre-Algebra topics but deeper• Important Topics include:

• Solving Equations (multi step, variables on both sides, no solution, infinitely many solutions)

• Solving inequalities• Solving systems of equations graphically and

algebraically• Slope-intercept form• Scatter Plots

Solving Equations

• Basic 2x + 5 = 12

• Intermediate 2(x+5)=6x+2

• Advanced ½(x + 5 + 6x) = 3(x + ½)

Solving Equations

• Special Solutions• 5x + 5 = 3(5x-4)-10x

• 3(2b-1)-7=6b-10

Solving Inequalities

• Solve same way as equations but with inequality sign.

• Remember: When multiplying or dividing by a negative number, the inequality sign changes

• Examples• 2x + 11 < 5x - 10• -2(4b+1) < -2b + 8• -12y – 24 > 42

Solving Systems of Equations

•3 Methods•Graphing •Substitution •Elimination

Solving Systems of Equations

• Graphic Organizer

Solving Systems of Equations

• Method 1• Graphing

• Best used when both equations can be easily solved for y

• Example 1: y = 2x + 3 y = -2x – 5

Solving Systems of Equations

• Method 1• Graphing

• Best used when both equations can be easily solved for y

• Example 2: 2x – y = -1 4x – 2y = 6

Solving Systems of Equations

• Method 2• Substitution

• Best used when one system is easily solved for y or x• Example 3: y = 5x + 1 4x + y = 10

Solving Systems of Equations

• Method 3• Elimination

• Addition- when coefficients are opposite• Example 4: 4x + 6y = 32 3x – 6y = 3

Solving Systems of Equations

• Method 3• Elimination

• Subtraction- when coefficients are the same• Example 5: 5m – p = 7 7m – p = 11

Solving Systems of Equations

• Method 3• Elimination

• Multiplication- when coefficients are different• Example 6: 5x + 6y = -8 2x + 3y = -5

Solving Systems of Equations

• Special Solutions

• No solution• Example 7: -3x + 3y = 4 -x + y = 3

• Infinitely many solutions• Example 8: 2x + 8y = 6 -5x – 20y = -15

Solving Systems of Equations

• Tool: Graphing CalculatorExample 1: y = 2x + 3 and y = -2x – 5 (-2,-1)Example 2: y = 2x + 1 and y = 2x – 3 No Solution Example 3: y = 5x + 1 and y = -4x + 10 (1,6)Example 4: y = -2/3x + 16/3 and y = 1/2x – ½ (5,2)Example 5: p = 5m – 7 and p = 7m – 11 (2,3)Example 6: y = -5/6x – 4/3 and y = -2/3x – 5/3 (2,-3)Example 7: y = x + 3 and y = x + 4/3 No Solution Example 8: y = -1/4x + ¾ and y = -1/4x + ¾ Inf. Many Sol.

Slope-Intercept Formy=mx+b

• Putting equations in slope intercept form given:• Slope and a Point• Example 1: (-2,5) Slope 3• Example 2: (4,-7) Slope -1

• Two Points • Example 3: (3,1) (2,4)• Example 4: (-1,12) (4,-8)

Slope-Intercept Formy=mx+b

• Putting equations in slope intercept form given:• Real World Data

• Example 1: In 1904, a dictionary cost $0.30. Since then the cost of a dictionary has risen an average of $0.06 per year.

• Write a linear equation to find the cost C of a dictionary y years after 1904.

• If the trend continues, what will the cost of a dictionary be in 2020.

Years after 1904

Cost

Slope-Intercept Formy=mx+b

• Putting equations in slope intercept form given:• Real World Data

• Example 2: Jackson is ordering tickets for a concert online. There is a processing fee for each order, and the tickets are $52 each. Jackson ordered 5 tickets and the cost was $275.

• Determine the processing fee. Write a linear equation to represent the total cost C for t tickets.

• Make a table of values for at least three other numbers of tickets.• Predict the cost of 8 tickets.

Slope Intercept Form

• Tool: Graphing Calculator

• Example 1: C=0.30 + 0.06y

• Example 2: C = 15t + 15

Scatter Plots• Scatter Plots show the relationship between a set of data

with two variables

• Graphic Organizer

Scatter Plots

• Scatter Plots- shows the relationship between a set of data with two variables, graphed as ordered pairs on a coordinate plane.

• Tool: Graphing Calculator

• Graph scatter plots and find line of best fit to predict data.

Scatter Plots

• Example 1: The table shows the largest vertical drops of nine roller coasters in the United Sates and the number of years after 1988 that they were opened.

• Identify the independent and dependent variables.• Is there a relationship between the data? If so, predict

the vertical drop in a roller coaster built 30 years after 1988.

Years since 1988

1 3 5 8 12 12 12 13 15

Vertical Drop (ft.)

151

155 225 230 306 300 255 255 400

Scatter Plots

• Example 2: The Body Mass Index (BMI) is a measure of body fat using height and weight. The heights and weights of twelve men with normal BMI are given in the table.

• Make Scatter Plot and Draw Line of Best Fit• Predict the normal weight for a man who is 84 inches tall.• A man’s weight is 188 pounds. Use the equation of the line

of fit to predict the height of the man.

Height (in)

62 63 65 67 67 68 68 68 68 72 73 73

Weight (Lb.)

115

124

120

134

140

138

144

152

147

155

168

166

Projects and Resources

• Stained Glass Window

• Wheel of Theodorus

• Kuta Software (worksheets)

• Math-Drills (worksheets)

• Khan Academy (Videos)

• Teachers pay Teachers

Thank you!