$100 $200 $300 $400 $500 $200 $300 $400 $500 sys. of eq. - graphing scatter plots sys. of...
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$100 $100 $100 $100 $100
$200
$300
$400
$500
$200 $200 $200 $200
$300 $300 $300 $300
$400 $400 $400 $400
$500 $500$500 $500
Sys. Of Eq. - Graphing Scatter Plots
Sys. Of Inequalities
Slope and y-intercept
Functions & Relations
Systems of Equations – Graphing for $100
What is the solution to the following system of equations shown by the graph:
Answer
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The lines intersect at the point (-3, 1)
Systems of Equations – Graphing
for $200What is the solution to the following
system of equations shown by the graph:
Answer
Back
There is no solution – the lines are parallel and thus they never intersect.
Systems of Equations – Graphing for $300
Write a system of equations to describe the following graph:
Answery = -x + 2 and y = 2x - 1
Back
Systems of Equations – Graphing for $400
Solve the following system of equations by graphing:
y = (1/2)x + 2y = (-3/4)x - 3
Answer
Back
y = (1/2)x + 2
y =(-3/4)x – 3
Solution:
(-4, 0)
Systems of Equations – Graphing for $500
Solve the following system of equations by graphing:
y = 2x - 53x + y = 0
AnswerSolve both equations for slope-intercept form:
3x + y = 0
-3x -3x
y = -3x
And
y = 2x -5
Solution:
(1, -3)
Back
Scatter Plots for $100
Does the following scatterplot show a positive, negative, or no correlation? How do you know?
Positive because as one variable increases the other variable also increases
Answer
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Scatter Plots for $200Make 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 15.5
8 21.5
10 26.5
12 34
14 33
16 37
18 41
Answer
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Scatter Plots for $300What is wrong with the following scatter
plot? (Name 2 things)
Answer
1)The line of best fit is not correct.2)There is no arrow at the end of the trend
line
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Scatter Plots for $400Use a graphing calculator to find the equation of
the line of best fit for the data.
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
y = –1.11x + 11.83
Answer
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Scatter Plots for $500Use a graphing calculator to find the equation of
the line of best fit for the data. GRAPH on your whiteboard
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
Back
Slope and y-Intercept for $100
Write the linear equation for slope-intercept form.
Answer
y = mx + b
Back
Slope and y-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
Back
Slope-intercept Form:
y = mx + b
So,
Y = -3x + 5
Slope and y-Intercept for $300
Write the equation of the line through points (2, 3) and (4, -1) in slope intercept form
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
Slope-intercept Form:
y = mx + b
3 = -2(2) + b
b = 3+4 = 7
y = -2x + 7
Answer
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Slope and y-Intercept for $400
Write the equation of the line in slope-intercept form:
The line through points
(-2, 3) and (0, -1)
AnswerPoint: (-2, 3) Point: (0, -1)
m = (y2 – y1)/(x2 – x1)m = (-1- 3)/(0 – -2) = -4/2 = -2Slope-intercept Form:y = mx + b-1 = -2(0) + b-1 = bThus, y = -2x - 1
Back
Slope and y-Intercept for $500
Write the equation of the line in slope intercept form:
AnswerSlope 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
Functions and Relations for $100
Define: Relation
Answer
Relation – A set of ordered pairs
Back
Functions and Relations for $200
Draw a mapping diagram for the following set of data. Is it a function?
(3,4)(2,1)(5,7)(3, -2)
No it is not a function because one input (3) goes to two outputs (4 and -2)
Answer
Back
235
Domain Range
-2147
Functions and Relations for $300
Write the following equation in function notation:
y = 3x - 4
Answer
y = 3x - 4
f(x) = 3x-4
Back
Functions and Relations for $400
Use the vertical line test to determine if the following graph is a function
Answer
Yes, it is a function because the vertical line never hits more than one point at a time.
Back
Functions and Relations for $500
Write the function rule from the given graph.
Answer
Two points on the graph: (0, -3) and (1, -1)m = (y2 – y1)/(x2 – x1)m = (-3 - -1)/ (0-1)m = -2/-1 = 2y = mx + by = 2x +b-3 = 2(0) + bb = -3f(x) = 2x - 3
Back
Systems of Inequalities for $100
Graph the following inequality:
y < -2x + 1
Answer
y < -2x + 1
Back
Systems of Inequalities for $200
Graph the following inequality:
y ≥ 3x + 3
Answer
y > 3x + 3
Back
Systems of Inequalities for $300Write an inequality to describe the
following graph:
AnswerThe line is dashed so it is < or >The graph is shaded above the line
meaning it is > or ≥Thus, it has to be > (The only one that
is for dashed and shaded above)The line has a y-intercept of -2 and a y-
intercept of -1, so the equation of the line is:
y > -x - 2
Back
Systems of Inequalities for $400
Graph the following system of inequalities:
y > -2x – 3
4x -2y ≥ 8
Answer
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Write both eq.’s in slope intercept form:
y > -2x – 3 and
4x -2y ≥ 8
-4x -4x
-2y ≥ -4x + 8
-2 -2 -2
y ≤ 2x - 4
Systems of Inequalities for $500Write a system of inequalities to
describe the following graph:
Answer
Back
y < -x + 2 and y ≥ 3x + 6