Download Jeapordy - Chapter 6

Rate of Change
and Slope
Intercept
Standard
Form and
Point Slope
Parallel and
Perpendicular
Lines
Scatter
Plots
Absolute
Value
Equations
$100 $100 $100 $100 $100
$200 $200 $200 $200 $200
$300 $300 $300 $300 $300
$400 $400 $400 $400 $400
$500 $500 $500 $500 $500
Rate of Change and Slope Intercept
for $100
Find the rate of change for the
following table and explain what
it means:
Time (Days) Cost ($)
3
75
4
100
5
125
6
150
Answer
m = (y2 – y1)/(x2 – x1)
m = (100- 75)/(4 – 3) =
25/1
Means the cost is $25
per day
Back
Rate of Change and Slope Intercept
for $200
Write the equation of the line
in slope-intercept form that
has a slope of -3 and a
y-intercept of 5
Answer
Slope-intercept Form:
y = mx + b
So,
Y = -3x + 5
Back
Rate of Change and Slope Intercept
for $300
Write the equation of the line in
slope-intercept form:
The line through points
(-2, 3) and (0, -1)
Answer
Point: (-2, 3)
Point: (0, -1)
m = (y2 – y1)/(x2 – x1)
m = (-1- 3)/(0 – -2) = -4/2 = -2
Slope-intercept Form:
y = mx + b
-1 = -2(0) + b
-1 = b
Thus, y = -2x - 1
Back
Rate of Change and Slope Intercept
for $400
Write the equation of the line
in slope intercept form:
Answer
Slope Intercept Form: y = mx +b
Pick two points on the line:
Points: (-4, -1) and (0, -2)
m = (y2 – y1)/(x2 – x1)
m = (-1- -2)/(-4 – 0) = 1/-4 = -1/4
B = -2 because that is y when x = 0
Thus, the equation of the line is
y = -1/4x - 2
Back
Rate of Change and Slope Intercept
for $500
Write the equation of the line
through points (2, 3) and (4, -1)
in point-slope form using the
point (2,3) AND then convert it
to slope intercept form
Answer
Slope Intercept Form: y = mx +b
Points: (2, 3) and (4, -1)
m = (y2 – y1)/(x2 – x1)
m = (3- -1)/(2 – 4) = 4/-2 = -2
Point-Slope Form: y – y1 = m(x – x1)
So, y – 3 = -2(x – 2)
y – 3 = -2x + 4
y = -2x + 7
Back
Standard Form and Point Slope for
$100
Write the formula for the
equation of a line in standard
form
Answer
Standard Form: Ax + By = C
where A, B, C are real numbers
and A and B are not both 0.
Back
Standard Form and Point Slope for
$200
Write the equation of the
line in point-slope
form:
The line through points
(2, -3) and (-2, 3)
Answer
Points: (2, -3) and (-2, 3)
m = (y2 – y1)/(x2 – x1)
m = (3- -3)/(-2 – 2) = 6/-4 = -3/2
Point-Slope Form:
y – y1 = m(x – x1)
where (x1, y1) is a point on the line
Thus, the equation of the line is
y – 3 = -3/2(x - -2)
y – 3 = -3/2(x + 2)
Back
Standard Form and Point Slope for
$300
Graph the following linear
equation using the
intercepts:
2x + 3y = 12
Answer
X int: 2x = 12; x = 6
Y int: 3y = 12; y = 4
Back
Standard Form and Point Slope for
$400
Rewrite the following equation
in standard form, using
integers:
y = -2/5x – (1/5)
Answer
y = -2/5x – (1/5)
5*y = 5*(-2/5)x – (1/5)*5
5y = -2x – 1
2x + 5y = - 1
Back
Standard Form and Point Slope for
$500
Write the linear equation from the
given graph using point-slope
form.
Answer
Two points on the graph: (0, -3) and (1, -1)
m = (y2 – y1)/(x2 – x1)
m = (-3 - -1)/ (0-1)
m = -2/-1 = 2
y – y1 = m(x – x1)
y - -3 = 2(x-0)
y + 3 = 2x
Back
Parallel and Perpendicular Lines
for $100
The product of the slopes
of two perpendicular lines
always equals _____?
Answer
The product of the slopes
of two perpendicular lines
always equals -1
Back
Parallel and Perpendicular Lines
for $200
Which 2 lines are
parallel?
a) 5y = -3x - 5
b) 5y = -1 – 3x
c) 3y – 2x = -1
Answer
Writing the lines in slope-intercept form:
a) 5y = -3x – 5
y = (-3/5)x – 1
b) 5y = -1 – 3x
c) 3y – 2x = -1
3y = 2x – 1
y = (2/3)x – (1/3)
a||b
y = (-3/5)x – (1/5)
Back
Parallel and Perpendicular Lines
for $300
Write the equation of the
line parallel to the given
line that passes through
the given point:
y = (1/3)x + 5
(-3, -3)
Answer
y = (1/3)x + 5
Parallel lines have the same slope
so the slope of the new line will
also be (1/3)
y = (1/3)x + b
Substitute in the point (-3, -3)
-3 = (1/3)(-3) + b
-3 = -1 + b
-2 = b
So, y = (1/3)x - 2
Back
Parallel and Perpendicular Lines
for $400
Write the equation of the
line perpendicular to the
given line that passes
through the given point:
y = (½)x - 3
(3, 6)
Answer
y = (½)x - 3
Perpendicular lines have slopes that
are negative reciprocals, so the
slope of the new line will be (-2)
y = (-2)x + b
Substitute in the point (3, 6)
6 = (-2)(3) + b
6 = -6 + b
12 = b
So, y = -2x + 12
Back
Parallel and Perpendicular Lines
for $500
Write the equation of a line
perpendicular to the
given line that intersects
the given line on the yaxis. Write your answer in
point-slope form:
y = 3x - 8
Answer
y = 3x – 8
So, m = 3, a point on the line = (0,-8)
Point-Slope Form:
y – y1 = m(x – x1)
y - -8 = 3(x – 0)
y + 8 = 3x
Slope of the Perpendicular line: (-1/3)
y + 8 = (-1/3)x
Back
Scatter Plots for $100
Define: Correlation
coefficient
Answer
Correlation coefficient: Tells how
closely the equation of a line of
best fit models the data in a
scatter plot. The correlation
coefficient is usually denoted
by the letter “r”
Back
Scatter Plots for $200
Make a scatter plot for the following data
comparing practice to score in a violin
competition, and draw in the trend line:
Practice (weeks)
Score
6
8
10
12
14
16
18
15.5
21.5
26.5
34
33
37
41
Answer
Back
Scatter Plots for $300
What is wrong with the
following scatter plot?
Answer
The line of best fit is not
correct.
Back
Scatter Plots for $400
Use a graphing calculator to find the equation of
the line of best fit for the data. Find the value
of the correlation coefficient r.
Average Speed (mi/h) Time (Hours)
8.5
2.5
7.5
3.75
6.5
4.5
6.0
5.0
5.5
5.5
5.0
6.25
4.0
6.75
3.5
8.75
Answer
y = –1.11x + 11.83
r = –0.9760964904
Back
Scatter Plots for $500
Use a graphing calculator to find the equation of
the line of best fit for the data. Find the value
of the correlation coefficient r. GRAPH
Year
Distance (meters)
0
31.9
1
31.55
2
34.45
3
31.6
4
34
5
36.15
6
35.05
7
38.7
Answer
y = 0.864x + 31.15
r = 0.8449426752
Back
Absolute Value Equations
for $100
Write the equation for the
parent function of an
absolute value equation:
Answer
y = |x|
Back
Absolute Value Equations
for $200
Explain how the following graph
compares to the graph of the
parent function:
y = |x| + 4
Answer
The graph shifts up 4 units
Back
Absolute Value Equations
for $300
Explain how the following graph
compares to the graph of the
parent function:
y = |x - 2| - 1
Answer
The graph shifts down 1 unit and
to the right 2 units.
Back
Absolute Value Equations
for $400
Graph: y = |x| - 5
Answer
Back
Absolute Value Equations
for $500
A ___________ is a shift of a
graph horizontally,
vertically, or both.
Answer
A translation is a shift of a
graph horizontally,
vertically, or both.
Back