Linear Relationships Notes - 4/26

Linear Relationships Notes - 4/26

Make sure to write down the notes! You get a grade for your notes so

PAY ATTENTION! Questions follow every slide to make sure you're paying attention! You are GRADED on your answers!

Graphing Equations

y = mx + b is on your STAAR Reference Sheet; just memorize what the letters represent.

m---> RATE OF CHANGE or how quickly the line rises or falls; RISE over RUN if positive, FALL over RUN if negative.

b ---> Y-INTERCEPT or where the line crosses the y-axis (where the RED dot is on the graph to the right)

Multiple Choice

What is RATE OF CHANGE?

• how quickly the line rises or falls.

• how much money you can exchange

• where the line crosses the y-axis

Multiple Choice

What is Y-INTERECEPT?

• how quickly the line rises or falls.

• how much money you can exchange

• where the line crosses the y-axis

Multiple Choice

Where can you find the y=mx+b formula?

• in your science class

• on your STAAR Reference Sheet

• No where

Graphing Equations

Make sure the label the x and y axis on your notes!

RATE OF CHANGE --> find two coordinates and count how much it rises and runs from dot to dot.

Rate is POSITIVE if rise/run

Rate is NEGATIVE if fall/run

Y-INTERCEPT --> look at where the line crosses the y-axis (see the green label on the picture)

Multiple Choice

If a RATE OF CHANGE is NEGATIVE, then which of the following is TRUE?

• Rate of change will be FALL over RUN

• Rate of change will be RISE over RUN

Multiple Choice

If a RATE OF CHANGE is POSITIVE, then which of the following is TRUE?

• Rate of change will be FALL over RUN

• Rate of change will be RISE over RUN

Multiple Choice

If a RATE OF CHANGE is NEGATIVE, then what will the line look like?

Multiple Choice

If a RATE OF CHANGE is POSITIVE, then what will the line look like?

Multiple Choice

Y-Intercept is where the line crosses...

• the y axis

• the x axis

Rate of Change

• Examples of RATE include:

• Miles per Hour

• Cost per Item

• Feet per Second

• The formula d = rt is on your STAAR Reference Sheet

• d = distance, r = rate, t = time

Multiple Choice

Which of the following is NOT an example of rate?

• feet per second

• miles per hour

• rate times time

• cost per item

Multiple Choice

Where can you find the formula d = rt?

• in your English class

• on a soccer field

• on your STAAR Reference sheet

• in your gym locker

Multiple Choice

What does the "d" stand for in the formula d = rt?

• distance

• rate

• time

• down

Multiple Choice

What does the "r" stand for in the formula d = rt?

• rate

• range

• time

• distance

Multiple Choice

What does the "t" stand for in the formula d = rt?

• rate

• temperature

• distance

• time

Rate of Change

• You can solve for any of the variables in d = rt, IF you know the other TWO variables.

• Remember a variable is a LETTER that represents an UNKNOWN NUMBER. (Example: d, r and t)

• On the GRAPH, you can see Distance = 150 and Time = 2

• 1) Substitute Numbers in d = rt formula

• 2) Divide both sides by 2; r=75

Fill in the Blank

You can solve for any of the variables in d = rt IF you know the other ___ variables.

Multiple Choice

On the example graph, miles is an example of ___ in the d = rt formula.

• d, distance

• r, rate

• t, time

Multiple Choice

On the example graph, hours is an example of ___ in the d = rt formula.

• d, distance

• r, rate

• t, time

Constant of Proportionality

• The formula k = y/x is found on your STAAR Reference sheet

• The definition is the ratio of the y-value to the x-value, represented by "k"; it is equal to the rate of change.

• k = rate of change = y/x

• When given a table, divide the y value by the x value (2/62, which is simplified to 1/31)

Multiple Choice

The constant of proportionality, or "k", is...

• x/y

• y/x

Multiple Choice

You can find the constant of proportionality, k = y/x....

• in your backpack

• on your STAAR Reference sheet

• in band class

Multiple Choice

k = y/x, which is ALSO equal to...

• y-intercept

• rate of change

• distance

Tables and Graphs

• X-values are...

• independent

• measured

• x-axis

• left side of table

• top row of table

Multiple Select

Check ALL that are TRUE for x-values

• independent

• dependent

• x-axis

• y-axis

• left side of table

Tables and Graphs

• Y-values are...

• dependent

• varies

• y-axis

• right side of table

• bottom row of table

Multiple Select

Check ALL that are TRUE for y-values

• independent

• dependent

• x-axis

• y-axis

• right side of table

Poll

Which of the things in this Quizziz confuses you the most?

• Nothing! I understand it all!

• Graphing Equations

• Rate of Change

• Constant Proportionality

• Tables and Graphs

Great job! Make sure you took notes!

Now, see how these notes help you solve problems!

Remember, that Tables, Graphs and Equations are all different ways to show the SAME information!

CARD 1

For your activity, you will be given a card that shows a DESCRIPTION, EQUATION, GRAPH and TABLE. Three of the four represent the SAME scenario. ONE is wrong. On your Recording sheet, explain which is wrong, how it should be fixed, and then find k = y/x and write the constant of proportionality.

Which one is WRONG?

On day 1, a plant has a height of 2 cm. It grows at a steady rate of 0.5 cm per week. SO, rate of change = 0.5. Y=intercept is 2 cm because when weeks (or x) = 0, y=2. The GRAPH is wrong because it shows the y-intercept as 0.5, when it should be 2. The graph should increase by 0.5 each week. Write down "GRAPH" as your answer for the next slide!

Multiple Choice

On the previous slide, which of the following did NOT match and was wrong?

• Description because plant height does NOT start at 2.

• Graph because it shows the y-intercept as 0.5, when it should be 2. The graph should increase by 0.5 each week.

• Equation because it shows the y-intercept as 0.5, when it should be 2.

• Table because it shows the y-intercept as 0.5, when it should be 2.

Which one is WRONG in Card 2?

Carefully look at the Card to the right.

Which one does NOT match?

Take your time and decide. You'll pick your answer on the next slide (for a grade!).

HINT: "Debits" means money is subtracted from an account.

Multiple Choice

On the previous slide, which of the following did NOT match and was wrong?

• Description

• Graph

• Equation

• Table

The TABLE is wrong in Card 2

Look at the Graph and Table, and the money definitely is increasing by $75 a month, but the Description says "Debits" and it should say "Credits" $75 each month. "Debit" means subtracting money while "Credit" means ADDING money.

Which one is WRONG? (Card 3)

Carefully look at the Card to the right.

Which one does NOT match?

Take your time and decide. You'll pick your answer on the next slide (for a grade!).

Also, find CONSTANT of PROPORTIONALITY (y value divided by x value)

Multiple Choice

On the previous slide, which of the following did NOT match and was wrong?

• Description because they went 45 miles per hour, not 55.

• Graph because it should start at (0, 55) NOT (0,0)

• Equation because it should be a y-intercept of + 55.

• Table because it has the x and y values in the wrong column.

Multiple Choice

On the previous slide (Card 3) what was the CONSTANT of PROPORTIONALITY? (y/x)

• 45

• 55

• 0

• -55

Which one is WRONG? (Card 4)

Carefully look at the Card to the right.

Which one does NOT match?

Take your time and decide. You'll pick your answer on the next slide (for a grade!).

Multiple Choice

On the previous slide, which of the following did NOT match and was wrong?

• Description because he wants to gain pounds each month

• Graph because it should start at (0,0)

• Equation because it should have a y-intercept of -320

• Table because it should begin at (0, 320) instead of (1, 320)

Which one is WRONG? (Card 5)

Carefully look at the Card to the right.

Which one does NOT match?

Take your time and decide. You'll pick your answer on the next slide (for a grade!).

Multiple Choice

On the previous slide, which of the following did NOT match and was wrong?

• Description because the rate is 15/60 NOT 15/30

• Graph because it should start at (0,0)

• Equation because it should be y = 15/30x + 60

• Table because it should begin at (0, 0) NOT (0, 60)

The EQUATION is wrong

If you look, the rate shows 15/60, but all other three show a rate of 15 ft per 30 minutes or 15/30. You need to change the rate and the y-intercept is 60. So the CORRECT equation is y = 15/30x + 60

You're done! If you have questions about linear equations and relationships, please email me!

Remember your grade for this slide show will GO IN THE GRADEBOOK. You may complete this slideshow a second time to improve your grade.