By: Jay Taylor
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Directions (cont.)
 View the instructions on how to complete each task
 After each lesson is viewed, watch the review video
 After watching the review video, take the quiz if you
feel ready to
 If you do not feel ready for the quiz, review the
material until you feel ready for the quiz.
 Good Luck!!!
Main Menu
How to solve
for “y” in
equations
How to graph
an equations
given an
equation with
“y” and “x”
variables
How to find
slope and
y-intercept
How to graph
functions from
y=mx+b form
Link to
Review Video
Link to quiz
How to Solve for “y” in an equation
3𝑦 + 7 = 𝑥 − 5
First Identify where “y” is in the equation
Solving for “y”
After “y” has been identified,
Solve for the “y” term by adding or subtracting the
constant in the equation
3𝑦 + 7 = 𝑥 − 5
-7
- 7
3𝑦 = 𝑥 − 12
Solving for “y”
Now to solve for “y” you must remove the attached coefficient
to “y”. To do that you must do the opposite operation which
here is dividing by 3.
3𝑦 = 𝑥 − 12
÷3
÷3___
𝑥
3
𝑦 = −4
Solving for “y”
Quick Review
Solve for y and click on the correct answer:
3
𝑦+9= 𝑥+3
2
2
A. 𝑦 = 3 𝑥 − 4
3
B. 𝑦 = 2 𝑥 − 9
2
C. 𝑦 = 3 𝑥 − 6
D. 𝑦 = 𝑥 − 4
3
E. 𝑦 = 2 𝑥 + 18
Oops!!! Wrong Answer
Hint: Don’t forget the distributive property
Oops!!! Wrong Answer
Hint: Don’t forget to multiply by the opposite
Great Job!!!
3
𝑦+9=𝑥+3
2
-9= -9
3
𝑦 =𝑥−6
2
2
2
× = ×
3
3
2
𝑦 = 𝑥−4
3
How to find slope and y-intercept
7
6
𝑦= 𝑥−
8
5
Finding Slope and y-intercept
7
6
𝑦= 𝑥−
8
5
This is written in y=mx+b form where m=slope and
b=y-intercept
Finding Slope and y-intercept
7
6
𝑦= 𝑥−
8
5
7
6
Where m= and b= −
8
5
Finding Slope and y-intercept
Quick Question
Find the slope and y-intercept and click on the correct answer
3
𝑦 =− 𝑥+8
4
A. slope=
3
4
and y-intercept= 8
3
B. slope= − 4 and y-intercept= 8
3
C. slope= − 4 and y-intercept= -8
3
D. slope= 8 and y-intercept= − 4
E. slope= 8 and y-intercept=
3
4
Oops!! Wrong Answer
Hint: Remember y=mx+b where m=slope and
b=y-intercept
Great Job!!!
3
𝑦 =− +8
4
y=mx+b
So m= slope and b= y-intercept
So this means m=
Slope=
3
−
4
3
−
4
and b= 8
and y-intercept= 8
How to Graph Functions (y=mx+b)
Identify slope and y-intercept
7
𝑦 =− +4
5
slope=
7
−
5
and y-intercept= 4
How to Graph a Function (y=mx+b)
y-intercept= 4 which
means the graph starts at
point (0,4)
(0,4)
How to Graph Functions (y=mx+b)
7
Slope= −
5
𝑟𝑖𝑠𝑒
𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑦
Slope=
or
𝑟𝑢𝑛
𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑥
Positive rise goes up, negative rise goes down.
So rise is -7 in this equation so go down 7 units.
Positive run goes right, negative run goes left
Then run is 5 so go to the right 5 units so make your
point there
How to Graph a Function (y=mx+b)
The slope can also be written as
7
−5
This means there are also points going up 7 units and
going to the left 5 units
How to Graph a Function (y=mx+b)
 Find 2 more points by
starting at (0,4)
 So to find the next point, go
down 7 units and to the
right 5 units from (0,4)
 To find the final point go up
7 units and to the right 5
units from (0,4)
 Connect the points with a
line
5
(-5,11)
7
(0,4)
7
5
(5,-3)
How to Graph a Function (y=mx+b)
Click on the correct graph for the function:
1
𝑦 = 𝑥−4
3
(-3,5)
(3,5)
(-3,3)
(3,-3)
(-3,-5)
(0,-4)
(0,4)
(0,4)
(-3,-3)
(0,-4)
(3,-5)
(3,3)
Oops!! Wrong Answer
Remember start at the y-intercept and slope=
𝑟𝑖𝑠𝑒
𝑟𝑢𝑛
Great Job!!!
1
3
m= and b= -4
Start at point (0,-4) go up 1 unit and to
the right 3 units make the point from
(0,-4), then go down one unit and to
the left 3 units from (0,-4)
How to Graph a Function
Solve for y
5𝑦 + 13 = 2𝑥 − 7
- 13
- 13
5𝑦 = 2𝑥 − 20
÷5 ÷5
𝑦=
2
𝑥
5
−4
How to Graph a Function
Identify slope and y-intercept
2
𝑦= 𝑥−4
5
Remember y=mx+b
2
5
Slope= and y-intercept= -4
How to Graph a Function
 After slope and y-intercept
is identified, draw the
graph
 Start at (0,-4) because yintercept=-4
2
5
 Because the slope= go up
2 units and to the right 5
units to get to point (5,-2)
 Because the slope can also
−2
be written as go down 2
−5
units and to the left 5 units
to get to point (-5,-6)
5
(0,-4)
(-5,-6)
5
2
2
(5,-2)
How to Graph a Function
Quick Question
Click on the correct graph for the eqaution:
7𝑦 + 12 = −3𝑥 + 61
(-7,10)
(0,7)
(0,7)
(7,4)
(7,10)
(-7,4)
(1,-4)
(-1,-4)
(0,-7)
(0,-7)
(-1,-10)
(1,-10)
Oops!! Wrong Answer
Hint: Start at the y-intercept and slope=
𝑟𝑖𝑠𝑒
𝑟𝑢𝑛
Great Job!!!
7y+12=-3x+61
-12
-12
7y=-3x+49
÷7 ÷7
3
7
y=− 𝑥 + 7
3
−
7
So slope=
and y-intercept= 7, giving you the points
(0,7), (-7,10), and (7,4).
Review Video
http://www.youtube.com/watch?v=jTs9OiK
7JDU
Quiz Time
Start
Quiz Question #1
Click on the correct answer by solving for y:
4y+3=3x-9
A. 𝑦 = 3𝑥 − 3
3
B. 𝑦 = 4 𝑥 − 12
3
2
C. 𝑦 = 4 𝑥 − 3
3
D. 𝑦 = 4 𝑥 − 3
2
E. 𝑦 = 3𝑥 − 3
Oops!!! Wrong Answer
Hint: Solve for 4y first
Great Job!!!
Move onto the next question
Quiz Question #2
Click on the correct answer by solving for y:
1
1
𝑦−1= 𝑥−2
4
3
4
A. 𝑦 = 3 𝑥 − 12
4
B. 𝑦 = 3 𝑥 − 4
1
C. 𝑦 = 3 𝑥 − 4
4
3
1
𝑥
3
D. 𝑦 = 𝑥 − 1
E. 𝑦 =
− 12
Oops!! Wrong Answer
1
Hint: Solve for 𝑦
4
1
opposite of is 4
4
first and then don’t forget the
Great Job!!!
Move onto the next question
Quiz Question #3
Click on the correct answer by identifying slope and
y-intercept:
2
𝑦 = 𝑥−3
3 2
A. Slope= 3 and y-intercept= 3
2
B. Slope= 3 and y-intercept= -3
3
C. Slope= 2 and y-intercept= 3
3
D. Slope= 2 and y-intercept= -3
2
E. Slope= -3 and y-intercept= 3
Oops!! Wrong Answer
Hint: Remember y=mx+b where m=slope and b=yintercept
Great Job!!!
Move onto the next question
Quiz Question #4
Click on the correct answer by identifying slope and
y-intercept:
𝑦 = −5𝑥 − 9
A. Slope= -9 and y-intercept=-5
B. Slope= 5 and y-intercept= 9
C. Slope= -5 and y-intercept= 9
D. Slope= -9 and y-intercept= 5
E. Slope= -5 and y-intercept= -9
Oops!! Wrong Answer
Hint: Remember y=mx+b where m=slope and
b=y-intercept
Great Job!!!
Move onto the next question
Quiz Question #5
Click on the correct graph from the function:
3
𝑦 = 𝑥+4
2
(2,7)
(-2,7)
(0,4)
(0,4)
(-2,1)
(2,7)
(2,-1)
(-2,-1)
(0,-4)
(0,-4)
(-2,-7)
(2,-7)
Oops!! Wrong Answer
Remember identify your slope and y-intercept first
Great Job!!!
Move onto the next question
Quiz Question #6
Click on the correct graph from the function:
1
𝑦 =− +1
3
(3,2)
(-3,0)
(-3,2)
(0,1)
(-3,0)
(0,-1)
(-3,-2)
(3,0)
(0,-1)
(3,-2)
(0,1)
(3,0)
Oops!! Wrong Answer
Remember identify your slope and y-intercept first
Great Job!!!
Move onto the next question
Quiz Question #7
Click on the correct graph of the function:
3𝑦 + 4 = −4𝑥 + 16
(-3,8)
(3,8)
(0,4)
(0,4)
(3,0)
(3,0)
(-3,0)
(-3,0)
(0,4)
(0,4)
(-3,8)
(3,-8)
Oops!! Wrong Answer
Remember to solve for 3y first
Great Job!!!
Move onto the next question
Quiz Question #8
Click on the correct graph of the function:
1
𝑦−7=𝑥−7
2
(-2,1)
(2,1)
(0,0)
(1,2)
(-1,-2)
(0,0)
(0,0)
(2,-1)
(0,0)
(-2,-1)
(1,-2)
(-1,-2)
Oops!! Wrong Answer
Remember to solve for y first
Great Job!!!
Move onto the end of the quiz
You Finished the Quiz
If you got 6 out of the 8 correctly you passed!!!
If not please review the material and retake the quiz.
Retake
quiz
Finish
Congratulations!!!
You have completed the lesson!
Finish