AAP

Multi-Step Equations and Linear Functions

Ms. Entrekin: AAP

Multi-Step Equations

• Isolate the variable

• Use opposite operations

• Addition

• Subtraction

• Multiplication

• Division

8q + 6 = 4q – 14

 3(x – 4) = 2(–2x + 1)

Fill in the Blank

Solve for y:

14 + 13y = 20y – 21

Fill in the Blank

Solve for b:

–15b + 21 + 5b = –19

Linear Functions

• When graphed create a line

• Highest exponent is 1

• Typically written in Slope-Intercept form

Slope-Intercept Form

• y = mx + b

• m is slope

• b is y-intercept

y-intercept

• Where line crosses y-axis

• y value when x = 0

• Starting point (in word problems)

Fill in the Blank

What is the y-intercept in this graph?

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What is the y-intercept in this graph? Write as an ordered pair

Fill in the Blank

What is the y-intercept of this graph? Write as an ordered pair

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An empty shipping box weighs 250 grams. The box is then filled with T-shirts. Each T-shirt weighs 132.5 grams. The equation W = 250 + 132.5T represents the relationship between the quantities in this situation, where W is the weight, in grams, of the filled box and T the number of shirts in the box. What is the y-intercept in this situation?

Slope

• Rise over run

• Δy/Δx

• Rate of change

• Pick points in the corners

What is the slope?

A battery is charged.

The percentage of the battery's capacity that is charged as a function of time (in minutes) is graphed.

Fill in the Blank

What is the slope of this line?

Multiple Choice

Suraj took a slice of pizza from the freezer and put it in the oven.

The pizza's temperature (in degrees Celsius) as a function of time (in minutes) is graphed. How fast did the oven heat the pizza?

• 8 degrees Celsius per minute

• 10 degrees Celsius per minute

• 0.9 degrees Celsius per minute

• 0.8 degrees Celsius per minute

Fill in the Blank

An empty shipping box weighs 250 grams. The box is then filled with T-shirts. Each T-shirt weighs 132.5 grams. The equation W = 250 + 132.5T represents the relationship between the quantities in this situation, where W is the weight, in grams, of the filled box and T the number of shirts in the box. What is the slope in this situation?

Multiple Choice

• y > 2x + 4

• y < -0.5x + 4

• y > -0.5x + 4

• y > -2x + 4

Simplifying Radicals

• Number inside is called radicand

• Break radicand down until you find perfect square

• Move square root of perfect square to the outside

 $\sqrt{50}$   

 $5\sqrt{63}$   

Multiple Choice

Simplify:

 $3\sqrt{80}$  

•  $4\sqrt{5}$  

•  $12\sqrt{5}$  

•  $6\sqrt{20}$  

•  $24\sqrt{10}$  

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