Download Graph each system using intercepts and label the solution to each

Solutions
Name _______________________________
Block _____ Date _________
Algebra: 6.2.1 Residual Plots
Bell Work: Graph each system using intercepts and label the solution to each system on its graph.
a.
2𝑥 − 𝑦 = 4
3𝑥 + 𝑦 = 1
x y
2 0
0 -4
x
𝟏
𝟑
y
0
0 1
𝑥 − 2𝑦 = 2
y
3
2
1
x
−4
−3
−2
−1
1
−1
−2
Solution: (𝟏, −𝟐)
−3
−4
y
b. 3𝑥 + 2𝑦 = 6
4
2
3
4
x y
2 0
0 -1
y
𝟐 0
0 3
x
4
3
2
1
−4
Solution: (𝟐, 𝟎)
−3
−2
−1
1
x
2
3
4
−1
−2
−3
−4
6-49. A residual plot can help you determine if a linear model is a good fit for a scatterplot of data. Whenever a
LSRL line is drawn on a scatterplot, a residual plot can also be created. A residual plot has an x-axis that is the
same as the scatterplot, and a y-axis that plots the residual.
a.
Match each scatterplot below with its corresponding residual plot.
b.
For which of the scatterplots does a linear model fit the data best? How does the residual plot help
you make that decision?
6-50. Help Giulia analyze the residuals for the pizza parlors described below.
a.
Create a scatterplot in the calculator. Find the residuals in the calculator (L3). If you want to purchase
an inexpensive pizza, should you go to a store with a positive or negative residual?
b.
What is the sum of the residuals?
c.
Make a residual plot using your calculator, with the x-axis representing the number of pizza toppings
(L1), and the y-axis representing the residuals (L3) . Interpret the scatter of the points on the residual
plot. Is a linear model a good fit for the data?
6-51. Dry ice (frozen carbon dioxide) evaporates at room temperature. Giulia’s father uses dry ice to keep the
glasses in the restaurant cold. Since dry ice evaporates in the restaurant cooler, Giulia was curious how long a
piece of dry ice would last. She collected the following data:
a.
What is the LSRL of this data?
b.
What is the correlation coefficient for this data? Is the
LSRL a good model? -0.998 Yes
6-52. A study by one state’s Agricultural Commission plotted the
number of avocado farms in each county against that county’s
population (in thousands). The LSRL isf = 9.37 + 3.96p where f is
the number of avocado farms and p is the population in thousands.
The residual plot is shown at right.
a.
Do you think a linear model is appropriate? Why
or why not?
b.
What is the predicted number of avocado farms
for the county with a population of 62,900
people?
c.
Using the residual plot, estimate the actual
number of avocado farms in the county with
62,900 residents.
y
4
6-53. Graph the inequality 𝑦 − 𝑥 > −3
3
𝒚>𝒙−𝟑
2
1
x
−4
−3
−2
−1
1
−1
−2
−3
−4
6-54. Solve and graph on a number line: 3𝑥 − 12 ≥ 5𝑥 + 18
−2𝑥 − 12 ≥ 18
−2𝑥 ≥ 30
𝒙 ≤ −𝟏𝟏
−17
−16
−15
x
−14
−13
2
3
4
6-55. Data for a study conducted on a vitamin supplement that claims to shorten the length of the common cold
is given in the table below:
a.
What is the equation of the line of best fit?
b.
How long do you predict a cold will last for a person who has
taken no supplement? Interpret the y-intercept in context. 5.37
c.
How long do you predict a cold will last for a person who has taken 6 months of
supplements? We cannot make a prediction with this model.
6-56. Write an explicit equation for the sequence graphed at right.
6-57. Graph the points (–3, 2) and (5, –4)
y
a.
Find the slope of the line determined by them.
b.
Write an equation for the line that contains the two points
4
3
2
1
Δ𝑦 −6 −𝟑
=
=
Δ𝑥
8
𝟒
𝑦 = 𝑚𝑚 + 𝑏
−3
(−3) + 𝑏
2=
4
9
2= +𝑏
4
8 9
= +𝑏
4 4
−1
=𝑏
4
𝑦 = 𝑚𝑚 + 𝑏
𝒚=
−𝟑
𝟏
𝒙−
𝟒
𝟒
x
−4
−3
−2
−1
1
−1
−2
−3
−4
2
3
4
6-58. Graph y = (x – 2)2 – 1. Label the vertex and roots of the graph.
y
4
How does this graph compare to the graph of the parent 𝑦 = 𝑥 2 ?
3
2
1
Vertex: (2, -1)
x
−4
Roots: 1 and 3
−3
−2
−1
1
2
3
−1
−2
The graph is 2 units to the right and 1 unit below the parent function.
−3
−4
6-59. Fill in the missing parts of each generic rectangle, and then write an equation showing the area as a
product and the area as a sum.
a.
𝟓𝟓 𝟏𝟏𝒙
𝟐
𝟐𝟐
b.
𝒙
𝟏𝟏𝟏
𝟑
𝟓
3𝑥
𝒙
𝟒𝟒
𝟒
6-60. Factor each quadratic expression completely
a.
7 7𝑥 −28
2
𝑥 𝑥
𝑥
−4𝑥
−4
𝑥 2 + 3𝑥 − 28
b.
(𝒙 − 𝟒)(𝒙 + 𝟕)
3𝑥 2 − 75
3(𝑥 2 − 25)
𝟑(𝒙 − 𝟓)(𝒙 + 𝟓)
6-61. Solve each equation below. (Check by graphing) Show Sufficient Work!!
a. 6 – (3 + x) = 10
b. 100(x + 3) = 200
c.
1
3
𝑥+4= 𝑥−2
d.
4
5
𝑥=
𝑥+2
45
4
6-62. Write a system of equations to solve.
Thanh bought 11 pieces of fruit and spent $5.60. If apples cost $0.60 each
and pears cost $0.35 each, how many of each kind of fruit did he buy?
System of Equations with variables defined.
𝑎 = # 𝑎𝑎𝑎𝑎𝑎𝑎
𝑝 = # 𝑝𝑝𝑝𝑝𝑝
𝒂 + 𝒑 = 𝟏𝟏
𝟎. 𝟔𝟔𝟔 + 𝟎. 𝟑𝟑𝟑 = 𝟓. 𝟔𝟔
�
1
0.6
𝑎
1
11
� ∙ �𝑝 � = �
�
0.35
5.60
6-63. Find the slope of the line through the points (6, –8) and (3, –4).
a.
Find the equation of the line through (6, –8) and (3, –4).
b.
Is the point (–3, 4) on the same line? How can you tell?
6-64. Consider the function 𝑓(𝑥) = |𝑥 + 3|
a.
b.
What is 𝑓(−2) = 1
If you take the absolute value of −2, and then then add 3, do you get the same result?
No, you get 5
6-65. Solve the system of equations by graphing (use intercepts):
𝑥+𝑦=4
𝑥 − 𝑦 = −2
y
4
𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆: (𝟏, 𝟑)3
2
1
x
−4
−3
−2
−1
1
−1
−2
−3
−4
2
3
4