Download Common Core Math I Standards: Unit 5 Test Review Guide

Common Core Math I Standards: Unit 5 Test Review Guide SOLUTIONS
Slope, Slope Intercept Form, Parallel + Perpendicular Lines
SLOPE:
Formula:
Points (x1, y1) and (x2, y2)
y 2  y1
x 2  x1
Concept:
Move in coordinate plane
Rate of Change:
Word Problems and Graphs
Quantity or Item
RISE Up or Down

RUN Right or Left
Time
SPECIAL SLOPES
ZERO or NO Slope:
o RISE = STAY and RUN = Left or Right
o Horizontal Line
o Equation of Line: y = number
UNDEFINED Slope:
o RISE = Up or Down and RUN = STAY
o Vertical Line
o Equation of Line: x = number
PARALLEL Slope:
o SAME (Identical) Slope
PERPENDICULAR Slope:
o Opposite Reciprocal Slopes
“Sign Change and Flip”
SLOPE INTERCEPT FORM: y = mx + b (m = slope and
b = y-intercept)
o Slope ALWAYS multiplies by x - variable
PRACTICE PROBLEMS:
1) Find the SLOPE between
a. (3, 2) and (7, 9)
240
92 7

73 4
38 5

 1
1  4
5
2) Rate of Change: Use the graph
a. What was the average rate of
change between 8:00 and 10:00 am?
135  90 45

 22.5
2 hours 2
Distance Traveled in Miles
b. (-4, 8) and (1, 3)
210
180
150
120
90
60
30
b. What is the rate of change between
11:00 and 12:00?
180  180 0
 0
1 hour
1
6:00
c. What was the average rate of change for the entire trip?
210  0 210

 26.25
8 hours
8
8:00
10:00
12:00
Time of Day
2:00
3) Determine slope and y-intercept of each equation.
6
c. 2 y  5 x  6
4
a. y   2 x
y

x

8
b.
5
5
3
y  x3
Slope = -2
4
2
Slope =
6
y-intercept =
3
5
5
Slope
=
y-intercept = 8
2
y-intercept = 3
d. y  3 x  7
y  7  3x
Slope = 3
y-intercept = 7
“y = mx + b and slope always multiplies by x”
4) Identify the slope of a line PARALLEL to each equation
Write equation in slope intercept form
Identify Slope
PARALLEL slope is SAME as original
a. y 
4
 3x
5
Parallel Slope = 3
b. 4 y  5 x  8
5
y  x2
4
Parallel Slope =
c. 3 y  2 x  6
2
y  x2
3
5
4
Parallel Slope =
2
3
5) Identify the slope of a line PERPENDICULAR to each equation
Write equation in slope intercept form
Identify Slope
Perpendicular slope is opposite reciprocal of original “SIGN and FLIP CHANGE”
6
a. y   x  4
7
Perpendicular Slope =
7
6
6) GRAPH each equation.
2
4a. y   x  3
3
Rise = -2  Down
Run = 3  Right
B = 3  Start
b. 3 y  8 x  12
8
y  x4
3
Perpendicular Slope = 
c. 2 x  5 y  3
2
3
y x
5
5
3
8
4b. y  4 x  2
Rise = 4  Up
Run = 1  Right
B = -2  Start
Perpendicular Slope = 
5
2
7) Write the equation of each graphed line in SLOPE INTERCEPT FORM.
a. m = 3 and (4, 7)
1
5
b. m = and (-2, 3)
c. m = and (-6, -8)
y = mx + b
4
2
7 = 3(4) + b
y

mx
b
y

mx

b
7 = 12 + b
1
5
1
-5 = b
3  ( 2)  b y  x  3.5
 8  ( 6 )  b y 
4
2
4
3


0
.
5

b

8


15  b
y = 3x – 5
3 .5  b
7b
d. Through (0, 5) and (2, 9)
e. Through (-1, 4) and (3, -2)
95 4
 2m
20 2
24 6 3


m
3  1
4
2
y  mx  b
y  mx  b
5  2( 0)  b
5 0b
y = 2x + 5
5b
Parallel Slope = 2 = m
y  mx  b
1 4b
y = 2x – 3
3b
2
h. Perpendicular to y   x  3 and
3
through (4, 7)
Perpendicular Slope =
y  mx  b
3
7  ( 4)  b
2
7  6b
1b
3
( 1)  b
2
4  1.5  b
4
y
3
x  2 .5
2
2.5  b
f. Parallel to y  2 x  5 through (2, 1)
1  2( 2)  b
5
x7
2
y
3
2
3
x 1
2
g. Parallel to 5 y  3 x  10 through (-5, 2)
3
Parallel Slope =
5
y  mx  b
3
3
2  ( 5 )  b
y

x5
5
5
2  3  b
5b
i. Perpendicular to 4 y  3 x  9 and
through (-6, 2)
Perpendicular Slope =
y  mx  b
4
2  ( 6 )  b
3
2  8  b
10  b
y
4
3
4
x  10
3