1.5 Algebra 2-use graphs and tables to approximate solutions

Multiple Choice

Do Now

Which of the following shows a linear equation?

Multiple Select

How would you describe your current mood?

• Happy and content

• Stressed and overwhelmed

• Bored and indifferent

• Anxious and worried

Multiple Select

 Which activity would you prefer to do right now?

• Hang out with friends

• Watch a movie or read a book

• Stay alone in your room

• Listen to music or go for a walk

Mini Review Graphing Linear Equations

Multiple Choice

What is our slope?

y = mx + b

• y

• m

• x

• b

Multiple Choice

What is our y-intercept?

y = mx + b

• y

• m

• x

• b

X and Y Intercepts

Linear equations have x and y-intercepts. The x-intercept is the x-coordinate of the point at which the graph crosses the x-axis. The y-intercept is the y-coordinate of the point at which the graph crosses the y-axis. 

Multiple Choice

What is the x-intercept of the graph?

• (5,0)

• (0,5)

• (0,4)

• (4,0)

Multiple Choice

What is the y-intercept?

• (0,15)

• (3,0)

• (15,0)

• (0,3)

Multiple Choice

What is the x-intercept?

• (-2,0)

• (0-6)

• (0,-2)

• (-6,0)

Multiple Choice

What is the y-intercept?

• (2,0)

• (0,2)

• (0,-2)

• (-2,0)

Graphing an Equation

You need only 2 points to graph a line. You can choose a value for x, and then evaluate for y.

Multiple Choice

What is the y-intercept in the equation y= -2x + 5

• -2

• 3

• 5

• Cannot be Determined

Multiple Choice

Find the slope

• -5/7

• 7/5

• -7/5

• 5/7

Multiple Choice

What is the slope in the equation y=2x + 3?

• 2

• 3

• 5

• Cannot be Determined

Multiple Choice

Which is the graph of y=-x+2?

• A

• B

• C

• D

Multiple Choice

Graph. y = 2/3x - 3

• a

• b

• c

• d

Multiple Choice

Do Now- Day 2

Give the equation for the graph

• y = 5x - 3

• y = 4x + 2

• y =-2x + 5

• y = - 2x + 4

Multiple Select

How would you describe your current mood?

• Happy and content

• Stressed and overwhelmed

• Bored and indifferent

• Anxious and worried

Quick Refresher Charts...

Make a Table of Values or T-Chart

Choose a value for x, plug in, and solve for y. Do this 2 or 3 times. Then, use the points to graph your equation.

Build a t-chart

Graph

Plot each ordered pair. Connect with a line.

Multiple Choice

A homeowner has 32 feet of fencing to build three sides of a rectangular chicken run. What is the significance of the point where the graph of area versus width intersects the x-axis?

• It represents the maximum area possible.

• It shows when the width is zero and no area is enclosed.

• It indicates the minimum amount of fencing needed.

• It marks the midpoint of the possible widths.

Multiple Choice

How can you use a graph to solve the equation -3x + 20 = 0.2x + 4?

• By finding the x-value where the two graphs intersect

• By finding the y-value where the two graphs intersect

• By finding the slope of the two lines

• By finding the midpoint of the two lines

Open Ended

Explain how you can verify the solution to a graphed equation by substitution.

Multiple Choice

What are the solutions to the equation |x - 4| = (1/2)x + 1 by graphing?

• x = 2 and x = 10

• x = 4 and x = 8

• x = 0 and x = 4

• x = 1 and x = 5

Multiple Choice

Solve the inequality x^2 - 4 > 0 by graphing. What intervals for x satisfy the inequality?

• x < -2 or x > 2

• x > 0

• x < 0

• x > -2 or x < 2

Fill in the Blank

The lines y = 60x and y = 40x + 40 intersect at the point (___, 120).

Multiple Choice

A motorcycle is 40 miles ahead of a car. If the car travels at 60 mph and the motorcycle at 40 mph, after how many hours will the car be ahead of the motorcycle?

• After 2 hours

• After 1 hour

• After 4 hours

• After 3 hours

Multiple Choice

Which method can be used to solve the inequality x^2 + 6x + 5 ≥ 0 as shown in the lesson?

• Graphing the equation and finding where it is above the x-axis

• Factoring the quadratic and solving algebraically

• Using the quadratic formula only

• Substituting values for x until the inequality is satisfied

Multiple Select

Which of the following steps are involved in approximating the solution to x^2 - 4x + 1 = x - 2 using a table?

• Identify the interval where the solution lies

• Check values of x within the interval

• Find where the values of the two functions are closest

• Graph the equation only

Open Ended

Explain how you would use a graph and a table together to solve the equation x^2 - 4x + 1 = x - 2. What are the advantages of using both methods?

Fill in the Blank

The equation x^2 - 4x + 1 = x - 2 has a second solution in the interval 4 < x < 5. Use a spreadsheet to approximate this solution to the nearest ___.

Multiple Choice

What are the approximate solutions to the equation -x^2 + 8x - 13 = |x - 4| as found using the INTERSECT feature on a graphing calculator?

• x ≈ 2.7 and x ≈ 5.3

• x ≈ 1.3 and x ≈ 4.7

• x ≈ 0.7 and x ≈ 6.3

• x ≈ 3.1 and x ≈ 7.2

Multiple Choice

Which of the following statements best describes how graphing can be used to solve equations and inequalities?

• By finding the points where two graphs intersect, you can determine the solutions to equations or inequalities.

• By drawing random lines and observing their slopes, you can solve equations.

• By only using tables of values, you can always find exact integer solutions.

• By comparing the colors of the graphs, you can solve equations.

Open Ended

What is an advantage of solving an equation graphically by finding the points of intersection?

Open Ended

Using the graph below, what is the solution to -2x + 4 = -2? How can you tell?

Open Ended

Exit Ticket

How can using graphs and tables help you approximate solutions to algebraic equations and inequalities?