Introduction to Solving Linear Equations

​Slope Intercept Form

​Linear Equations

• ​A linear equation is an equation that forms a straight line when graphed on a coordinate plane. We know it as writing our "RULE" when given a table of values.

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• ​Slope Intercept form is a type of linear equation written as y = mx + b

​Y - intercept

• ​The y-intercept is the number in place of "b" in y=mx+b

• This is your initial starting value, and is the starting point when graphing a line!

• The y-intercept is w​here the line will cross through the y-axis on the coordinate plane.

• Pay attention to the symbol in front of b in the equation! This tells you if it is positive or negative (y=3x-4 means b = -4)​

• The y-intercept is written as an ordered pair (0 , b). Thus, if b = -4 the ordered pair is (0, -4)

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​Slope

Multiple Choice

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

• 2
• 3
• 5
• Cannot be Determined 

Multiple Choice

What is the slope in the picture?

• Positive
• Negative
• Zero
• Undefined

Multiple Choice

What is the slope?

• Positive
• Negative
• Zero
• Undefined

Multiple Choice

Determine the slope and y-intercept from the following equation:   $$y=\frac{3}{2}x+3$$  

• slope: 3   y-intercept:  (0,2) 

• slope: $$\frac{3}{2}$$    y-intercept:  (0,3) 

• slope:  3  y-intercept:  (0, $$\frac{3}{2}$$  )

• slope: 1   y-intercept:  (0,3) 

Multiple Choice

Which letter in the equation below represents the slope?

y=mx+b

• y

• m

• x

• b

Multiple Choice

Which number or letter represents the y-intercept? $$y=\frac{1}{2}x-6$$  

• y

• $$\frac{1}{2}$$  

• x

• -6

Multiple Choice

What is the equation of a line with a slope of 4 and a y-intercept of 2?

• y = -4x + 2

• y = -2x + 4

• y = 4x + 2

• y = 2x + 4

Multiple Choice

Write the equation that represents this word problem:

Miles makes tacos at a restaurant. He has already made 8 tacos, and can make 3 tacos per minute.

• y= 8x + 3x

• y= 3x + 8

• y= 8x + 3

• y= 3 + 8

Multiple Choice

Write the equation that represents this word problem:

Nicholas received $100 for his birthday. He decides to spend $20 per day on whatever he wants.

• y= 20x + 100

• y= -20x - 100

• y= 20x - 100

• y= -20x + 100

Multiple Choice

Find the unit rate.

18 orders in 3 days = ________ orders per day

• 3

• 9

• 6

• 8

Multiple Choice

The Williams family bought four concert tickets for $252.  What was the price per ticket?

• $62.00

• $6.30

• $63.00

• $60.00

Multiple Choice

 if there are 5 boys for every 7 girls in math class, how many boys are there if there are 35 girls?

• 20
• 25
• 30
• 35

Multiple Choice

In an animal shelter, the ratio of dogs to cats is 5 to 3. There are 25 dogs.  Write and solve a proportion to find the number c of cats.

• c=15
• c=18
• c=21
• c=16

Multiple Choice

John's mother age is 5 years more than the three times of John's present age. Find John's present age , if his mother is 44 years old.

• $$13$$  

• $$15$$  

• $$29$$  

• $$39$$  

Multiple Choice

The larger of two numbers is two more than five times the smaller number. If the sum of the two numbers is 80, find both numbers.

WHICH EQUATION WOULD LET YOU FIND THE SMALLER NUMBER?

• x+2=80

• 5x+2=80

• x+5x+2=80

Multiple Choice

The larger of two numbers is two more than five times the smaller number. If the sum of the two numbers is 80, find both numbers.

• 11 and 57

• 20 and 105

• 16 and 70

• 13 and 67