Slope Intercept Form Packet
Name:___________________________
This packet is a REVIEW of material from unit 6.
During PARCC week you will be in class on some days but will
not have math on others. Bring this packet with you on the days
you have math and you will be able to use that class time to work
on it. On days that you do not have math, you will need to do
some work on your own time. The packet is due on MONDAY
March 20 at the beginning of class regardless of the number of
days you are in class.
This is a review and should not be too time consuming!
1
Proportional Relationships
Example
The height of a hot air balloon after a few seconds is
shown. Determine whether the relationship between
the two quantities is proportional. Explain or prove.
1. CHECK FOR CONSTANT RATE OF CHANGE
The constant rate of change is or 9 feet per second
2. CHECK FOR CONSTANT RATIOS Y/X
9/1 = 9 18/2 = 9 27/3=9 36/4 = 9
Since all the ratios are equal they have constant ratios.
Time (s)
Height of Hot
Air Balloon (ft)
1
2
3
4
9
18
27
36
The relationship IS
proportional
Practice
Determine whether the relationship between the two quantities described in each table is Proportional. Explain or
prove.
1)
2)
3)
4)
Party Table Rental
Number of Tables Cost($)
2
12
5
30
8
48
11
66
2
The Slope of a line
Positive Slopes go up from left to right
Negative Slopes go down from left to right
Horizontal Lines have a slope of zero
Vertical Lines have an undefined slope (or no slope)
Slope is always notated by the lower case “m”
Slope = change in y = vertical change = rise
change in x = horizontal change
run
Slope Formula
To find a slope given two ordered pairs (x1,y1), (x2,y2), use the slope formula:
m = y2 – y1
x2 – x 1
Find the slope given two points:
(x1,y1) (x2,y2)
1) (9, 5) (4, 8)
2) (6 , -3) (4, - 5)
m=8–5 = 3
4–9
-5
m = -5 – -3
4–6
= -5 + 3 = -2 = 1
4–6
-2
Try These: Check your answer at the bottom of the page before going on.
1) (4, 3) (7, 2)
2) (-6, 10) (-4, 8)
3) (-7, 2) (-7, 4)
1) m =
−
3
2) m = -1 or
−
2
3) m = = 𝑢𝑛𝑑𝑒𝑓𝑖𝑛𝑒𝑑 𝑠𝑙𝑜𝑝𝑒
0
3
PRACTICE: Name the type of slope each line below has:
1)
2)
_________
3)
_________
Find the slope given two points:
1. (2, 3) (9, 7)
=
4)
_________
_________
−
−
2. (3, 4) (4, 6)
m = _________
m = _________
3. (2, 6) (-1, 3)
4. (-3, -4) (5, 1)
m = _________
m = _________
5. (5, 7) (-2, -3)
6. (-2, 3) (8,3)
m = _________
m = _________
4
Slopes from Graphs
a) Choose two points on the line
b) Find the Rise: count from the lower point up to where the upper point is
c) Find the Run: count right or left to the second point
- Right is a positive run
- Left is a negative run
m=2=2
1
m = 1 = -1
-1
Try These: Check your answers at the bottom of the page before going on.
m=
m=
2
1) m = =
4
2
2) m =
−3
5
Determine the slope of each line. Use the points given. (Reduce if possible)
1.
2.
3.
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
4.
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5.

6.
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
7.
8.
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9.

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10.
11.
12.

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6
Slopes from tables
Example
1. The table shows the cost of using a computer at an Internet café for a given amount of time.
Find the rate of change in cost with respects to time
Time(hours) 2
4
6
Cost(dollars) 7
14 21
= =
=
Practice: DON”T FORGET TO LABEL!!!!!
2. The table shows the distance a person walks for exercise. Find the rate of change in distance
with respect to time.
Time(minutes)
30 60
90
Distance (miles)
1.5
3
4.5
3. The table shows the cost to paint a house for a given number of hours. Find the rate of change
in cost with respect to time .
Time(hours) 4
6
8
Cost(dollars) 90 135 180
4. The table shows the number of days you keep a rented movie before returning it and the total
cost of renting the movie. Find the rate of change in cost with respect to time and interpret its
meaning.
Time(days)
4
5
6
7
Total Cost(dollars) 6.00 8.25
10.50
12.75
5. The table shows the amount of time spent at an amusement park and the admission fee the
park charges. Find the rate of change in the fee with respect to time spent at the park and
interpret its meaning.
Time(hours)
4
5
6
Admission Fee(dollars)
34.99 34.99
34.99
7
Intercepts of a Linear Equation
x intercept
The x intercept is the point where the line crosses the
x axis. At this point y = 0.
y intercept
The y intercept is the point where the line crosses the
y axis. At this point x = 0.
Consider the following equation:
6x + 3y =18
To find the x intercept set y = 0.
To find the y intercept set x = 0.
6x + 3(0) = 18
6x = 18
x = 3
The x intercept is (3,0)
6(0) +3y = 18
3y = 18
y = 6
The y intercept is (0,6)
Try This one: Check your answers at the bottom of the page before going on. SHOW all work!
Find the x and y intercepts of the equation 3x + 5y = 30
x –intercept = (10, 0)
y-intercept = (0, 6)
8
Practice: Find the X and Y-intercepts, then graph using the intercepts
1) 6x – 8y = 24
x- int ________
y- int ________
2) 14x + 7y = 28
x- int ________
y- int ________
3) 3x + 2y = 6
x- int ________
y- int ________
9
Slope-intercept form
The Equation of a line is y = mx + b (This is called slope-intercept form)
m= slope = rise
run
Positive rise goes up
Positive run goes right
Negative rise goes down
Negative run goes left
b = y-intercept (where the line crosses the y-axis)
(x,y) represent all of the points on the line
How to graph a line given the equation y = mx + b
1) Solve the equation for y = mx + b
2) Graph the y-intercept (b)
3) Graph the slope (m), starting from the y-intercept
4) Draw a line through the two points
Examples:
1) m = -4/1
b=2
y = -4x + 2
2) m = ½ b = 3
y=½x+3
10
Practice:
Graph the following given a slope and a point:
1) m = - ½
b=2
2) m = 6,
b = -3
3) m =0 , b = 4
Graph the following equations of lines: (Hint: Determine the slope and y-intercept)
4) y = -4x + 5
7) y = - 5/2x + 3
5) y = 3/4x – 1
8) y = -4x
6) y = 2x - 2
9) y = 3x - 3
11
Writing Equations from Graphs
How to find the equation from graph
a) Find the slope (Rise/Run): slope = m
b) Find the y-intercept (Where the line crosses the y-axis: y-intercept = b
c) Plug the slope (m) and the y-intercept (b) into y = mx + b
a) Find slope
m = 1/1= 1
b) Find y-int
c) y = mx = b
b=3
y = 1x + 3
2
1
= 
4
2
b) b = -2
c) y = - ½x – 2
a) m =
a) m =
b) b =
c) y =
Practice : Finding Slope-intercept Form
I. Determine the slope and y –intercept for each line shown. Then write the equation of the line
1. y = ____________
m = _____ b = ____
2 . y = ____________
m = ______ b = _____
3. y = ____________
m = ______ b = _____
12