•1. Plot the point (-4, 3) in a rectangular coordinate system.
•2. Graph the line 3x + 2y = 6.
Graph the line using (0,3) and (2,0)
•3. Test the equation for symmetry with respect to the x-axis, the y-axis, and the origin.
x2 + y2 + x2y2 = 4
symmetry with respect to the x-axis
if (x,y) satisfy equation then (x,-y) satisfy the equation
if x2 + y2 + x2y2 = 4then
x2 + (-y)2 + x2(-y)2 = x2 + y2 + x2y2=4 so
Yes, the graph of the equation is symmetrical respect to the x-axis
symmetry with respect to the y-axis
if (x,y) satisfy equation then (-x,y) satisfy equation
if x2 + y2 + x2y2 = 4then
(-x)2 + y2 + (-x)2y2 = x2 + y2 + x2y2 =4 so
Yes, the graph of the equation is symmetrical respect to the y-axis
symmetry with respect to the origin
if (x,y) satisfy equation then (-x,-y) satisfy equation
if x2 + y2 + x2y2 = 4then
(-x)2 + (-y)2 + (-x)2(-y)2 = x2 + y2 + x2y2=4 so
Yes, the graph of the equation is symmetrical respect to the origin
•4. Test the equation for symmetry with respect to the x-axis, the y-axis, and the origin.
x2 + xy2 + x = 2
•5. Test the equation for symmetry with respect to the x-axis, the y-axis, and the origin.
x2 + xy2 + 2y = 1
symmetry with respect to the x-axis
if (x,y) satisfy equation then (x,-y) satisfy equation
if x2 + xy2 + 2y = 1 then
x2 + x(-y)2 + 2(-y) = x2 + xy2 -2y (is not original equation)
No, the graph of the equation is not symmetrical respect to the x-axis
symmetry with respect to the y-axis
if (x,y) satisfy equation then (-x,y) satisfy equation
if x2 + xy2 + 2y = 1 then
(-x)2 + (-x)y2 + 2y = x2 -xy2 + 2y(is not the original equation)
No, the graph of the equation is not symmetrical respect to the y-axis
symmetry with respect to the origin
if (x,y) satisfy equation then (-x,-y) satisfy equation
if x2 + xy2 + 2y = 1 then
(-x)2 + (-x)(-y)2 + 2(-y) = x2 -xy2 -2y(is not the original equation)
No, the graph of the equation is not symmetrical respect to the origin
•6. Find the distance between (-6, 4) and (0, -4).
d((-6,4),(0,-4))=
Answer: 10
•7. Find the midpoint of the line segment with endpoints (-5, -5) and (7, 9).
Midpoint = ((-5+7)/2,(-5+9)/2)=(1,2)
Answer: (1,2)
•8. Find the center and radius of the circle.
(x + 5)2 + (y - 3)2 = 49
If equation is (x-a)2+(y-b)2=r2
Then center is (a,b) and radius =r
(x + 5)2 + (y - 3)2 = 49
(x – (-5))2 + (y - 3)2 = 72
Answer: Center is (-5,3), radius is 7
•9. Find the center and radius of the circle.
3x2 + 3y2 - 18x + 6y - 162 = 0
If equation is: x2+y2+ax+by+c=0
center is (–a/2,-b/2)
r=
3x2 + 3y2 - 18x + 6y - 162 = 0
Then
x2 + y2 - 6x + 2y - 54 = 0
a=-6, b=2, c=-54
Center is (-(-6)/2,-2/2)=(3,-1)
Radius =r===64=8
Answer: center is (3,.1) and radius is 8
•10. Find the equation of a circle with center (2, -3) and the graph of which contains the point (3, 4).
Radius=r=
Answer: (x-2)2+(y+3)2=2
•11. Indicate the slope.
3x + 4y = 12
y=(-3x+12)/4= (-3/4)x+3
Answer: slope is -3/4
•12. Find the equation of the line with slope -6 and y-intercept 3. Write the equation in standard form Ax + By = C, A 0.
Y=-6x+3
y+6x=3
Answer: 6x+y=3
•13. Write the equation of the line with slope 0 and y-intercept -7. Write the equation in standard form Ax + By = C, A 0
Y=-7
Answer: y=-7
•14. Write the equation of the line passing through (0, -5) and (0, 1).
Slope is (1-(-5))/0 undefined
Answer: x=0
•15. The Number Two Plumbing Co. charges $45 per hour plus a fixed service call charge of $65. Write an equation that will allow you to compute the total bill for any number of hours, x, that it takes to complete a job.
Y=total bill
Answer: y=45x+65
•16. A business purchases a copier for $5,500 and anticipates it will be worth $2,500 after 10 years. Use straight-line depreciation to find a linear model for the depreciated value V of the copy machine after t years of use. (Points: 5
Y=5500-300x
•17. The regression model for the data shown in the table is y = 2.3x + 3.9
x / y4 / 14
1 / 6
3 / 9
2 / 9
5 / 17
7 / 20
6 / 16
Use the model to estimate y when x = 3.5.
y = 2.3x + 3.9, if x=3.5 then y=2.3(3.5)+3.9=11.95
Answer: 11.95
18. The regression model for the data shown in the table is y = -3.0x + 134.6.
x / Y10 / 114
8 / 108
15 / 77
14 / 87
20 / 75
17 / 94
Use the model to estimate y when x = 45.
y = -3.0x + 134.6, if x=45 then y=-3.0(45)+134.6=-0.4
Answer: -0.4
19. Find a linear regression model for the data. Round regression coefficients to two significant digits.
x / y2 / 15
5 / 12
6 / 16
11 / 14
12 / 20
15 / 35
20 / 38
21 / 42
24 / 47
Answer: y=1.67x+5.08
20. The data in the table shows the height x (in inches) compared to the shoe size y worn for a random sample of 12 males.
x / y64 / 9
66 / 10
67 / 9.5
76 / 11.5
71.5 / 13
62 / 9
65.5 / 11
68 / 10.5
73 / 12
63 / 12
70 / 11
65 / 10
Find a linear regression model for the data.
Answer: y=0.18x-1.45