Deck 4: Lines parabolas and Systems

Question 1

Find the slope of the line 3x + 9y - 7 = 0.

Answer 1

-

Question 2

The slope of the line passing through the points (4,9)and (6,k)is 5.Find k.

Answer 2

19

Question 3

The equation of a certain line is 3(x - 4)- (y + 1)= 4.Find: (a)the slope-intercept form and (b)a general linear form.

Answer 3

(a)y = 3x - 17
(b)3x - y - 17 = 0

Question 4

Sketch the graph of x = 4.

Question 5

What is the slope of a horizontal line?

Question 6

Find the slope of the line 4x - 8y + 5 = 0.

Question 7

The slope of a certain line is 4.If the x-value of a point on the line increases by 3 units,by how many units does the y-value increase?

Question 8

Find the slope of the line passing through the points (5,-3)and (2,-1).

Question 9

For the straight line 2x + y - 3 = 0 find: (a)the slope; (b)the y-intercept; and
(c)sketch the graph.

Question 10

Graph the equation 5x + y + 8 = 0.

Question 11

Graph the equation 3x + 4y - 12 = 0.

Question 12

The diagram below shows lines with slopes 0,1,-1,3,and -3.What is the slope of (a)line
and (b)line
?

Question 13

The equation of a certain line is y + 2 = -2(x - 3).Find: (a)the slope-intercept form and (b)a general linear form.

Question 14

Find an equation of the line that passes through the origin and that has slope -5.

Question 15

Find the slope-intercept form of an equation of the line that passes through the point (2,0)and has slope 4.

Question 16

Find the equation of the line with y-intercept 4 and slope -
.

Question 17

Sketch the graph of 5(x + 3)- 3(y - 1)= 0.

Question 18

For the line y = 7x - 3,find (a)the slope and (b)the y-intercept.

Question 19

Find the slope of the line passing through the points (3,9)and (2,-5).

Question 20

Sketch the graph of y = 3.

Question 21

Find the slope-intercept form of the line that passes through (2,-3)and (-4,7).

Question 22

Find a general linear equation of the line that passes through the points (-2,5)and (5,2).

Question 23

A general linear equation of the line that has slope -2 and that passes through the point (1,3)is

A) 2x + y + 1 = 0.
B) 2x - y + 1 = 0.
C) 2x + y - 7 = 0
D) 3x + y + 5 = 0
E) 2x + y - 5 = 0

Question 24

Find a general linear equation of the line that passes through point (1,-2)and has slope 3.

Question 25

The slope and y-intercept of the line 6x - 5y + 4 = 0 are

A) and 4, respectively.
B) -5 and 4, respectively.
C) and , respectively.
D) - and , respectively.
E) and , respectively.

Question 26

The slope of the line 4x + 5y + 3 = 0 is

A) 4.
B) -4.
C)
D) -
E) -

Question 27

Find a general linear equation of the line that passes through point (-6,4)and has slope -2.

Question 28

A line passes through the points (1,1)and (9,8).The point on it that has a y-coordinate of -6 is

A) (-7, -6).
B) (6, -6).
C) (-5, -6).
D) (4, -6).
E) (5, -6).

Question 29

Determine an equation of the vertical line that passes through the point (3,-6).

Question 30

Find an equation of the horizontal line that passes through the point (5,6).

Question 31

An equation of the line with slope 8 and y-intercept 5 is

A) y = 8x + 5.
B) y = 5x + 8.
C) 8x + 2y + 5 = 0.
D) 5x - 3y + 8 = 0.
E) 16x - 2y + 5 = 0.

Question 32

The y-intercept of the line 3x + 5y + 4 = 0 is

A) 4.
B) -4.
C)
D) -
E) -

Question 33

The slope of the line 4x - 8y + 3 = 0 is

A) 2.
B) -2.
C)
D) -
E) 4.

Question 34

The slope of the line passing through the points (-4,5)and (3,-2)is

A) 1.
B) -1.
C) 3.
D) -3.
E) -7.

Question 35

Which of the following statements are true?
I.Slope is not defined for a vertical line.
II.A line that falls from left to right has a negative slope.
III.A line with slope
Is more nearly horizontal than a line with slope
)

A) I only
B) II only
C) I and II only
D) I and III only
E) all of the above

Question 36

An equation of the straight line passing through (1,-5)and (-2,4)is

A) x - 3y + 2 = 0.
B) x - 3y - 16 = 0.
C) x + 3y - 14 = 0.
D) 3x + y - 5 = 0.
E) 3x + y + 2 = 0.

Question 37

Find a general linear equation of the line that passes through the points (4,-3)and (6,-7).

Question 38

Find the slope-intercept form of the line that passes through (0,4)and (1,1).

Question 39

The y-intercept of the line determined by the points (-1,-4)and (-2,5)is

A) 7.
B) -7.
C) 13.
D) -13.
E) -15.

Question 40

The slope of the line x = 2 is

A) 0.
B) 2.
C) -2.
D) 3.
E) not defined.

Question 41

Determine whether the following lines are parallel,perpendicular or neither.
3x - 2y = 19
2x + 3y = 4

Question 42

Determine the equation of the line which is perpendicular to 2x - y + 3 = 0 and has y-intercept 6.

Question 43

Find the x-intercept made by the line that passes through the points (1,-1)and (-1,0).

Question 44

Determine whether the following lines are parallel,perpendicular or neither.
0.21x - 0.35y + 8 = 0
x + 0.6y - 9 = 0

Question 45

Determine whether the following lines are parallel,perpendicular or neither.
3x - 2y = -1
2x + 3y = -20

Question 46

Determine whether the following lines are parallel,perpendicular or neither.
3x - 4y = 3
12x + 6y = 12

Question 47

Find the equation of a line having slope = 1 and x-intercept = -2.

Question 48

Determine whether the following lines are parallel,perpendicular or neither.
12x + 4y = 16
24x + 8y = 36

Question 49

Find the slope and y-intercept of a line 2y + 3(x - 1.9)= 0.

Question 50

Determine whether the following lines are parallel,perpendicular or neither.
12x + 4y = 16
15x + 5y = 23

Question 51

Determine whether the following lines are parallel,perpendicular or neither.
0.1x - 7y + 81 = 0
2x - 140y + 9 = 0

Question 52

In 1986 the stock in a biotechnology company traded for $30 per share.In 1996 the company started having trouble,and the stock price dropped to $10 per share.Use a graphing calculator to show the relationship between price per share and the year in which it traded.Find and interpret the slope.

Question 53

Find the equation of a line which is parallel to the line 2x + 3y - 7 = 0 and passes through the point (-1,2).

Question 54

10 square yards of a good quality wool carpet costs $400 and 20 square yards costs $800.Use a graphing calculator to show the relationship between cost and amount purchased.Find and interpret the slope.

Question 55

Find the equation of a line which is parallel to the line x = 0.521 and passes through the point (0.1,-7).

Question 56

Find the equation of a line having slope = 0.5 and x-intercept = 1.8.

Question 57

Find the equation of a line having slope 0.5 and x-intercept = 1.3.

Question 58

Find the equation of a line which is perpendicular to the line 2x + 3y - 57 = 0 and passes through the point

Question 59

Find the equation of a line which is perpendicular to the line x = 0.521 and passes through the point (0.1,-7).

Question 60

A line has slope and passes through the point (4,2).The point on the line that has its second coordinate equal to -5 is

A)
B)
C)
D)
E)

Question 61

A bank charges $10 for a money order.What is an equation for the relationship between the fee F charged and the amount of the money order?

Question 62

A mathematical model can approximate the winning distance for the Olympic discus throw by the formula d = 175 + 1.75t,where d is in feet and t = 0 corresponds to the year 1948.We might want to predict in what year a certain distance will be exceeded,so rewrite the equation to solve for t.Use a graphing calculator to graph the resulting equation and find the coordinates of any two points on the line and use them to estimate the slope.Compare this with your answer.

Question 63

The stock price of a company has risen at the rate of $5.00 per month over the last year.On January 1 it was $75.00.Write an equation that shows this relationship.

Question 64

Graph the general linear form of the equation for the size of a human fetus more than 12 weeks old whose slope-intercept form is L = 1.53t - 6.7.

Question 65

An orthodontist charges $3000 for the phase of treatment for a nine-year old which will provide better alignment and more room for permanent teeth in the future.What is an equation for the relationship between cost C of the treatment and the number of visits required to attain the desired result?

Question 66

Graph the general linear form of the Fahrenheit-Celsius conversion equation whose slope-intercept form is

Question 67

The relationship between temperature on the Fahrenheit scale and the temperature on the Celsius scale is
Find the slope and y-intercept of the equation.

Question 68

Graph the general linear form of the Olympic discus throw equation whose slope-intercept form is

Question 69

The area of rain forest in a South American country has decreased by 500 acres per year for the last 10 years.It had 12,000 acres 10 years ago.Use a graphing calculator to graph the resulting equation and determine when all of the rain forest in this country will be destroyed.

Question 70

The price of computer technology has been dropping steadily for the past ten years.The price of a certain desktop PC has decreased by $650 per year during this time period.If this PC sold for $6770 ten years ago,what equation describes the cost C of the PC over the last ten years? Graph your equation on a graphing calculator.Can you predict the price of a desktop PC a few years into the future
with this model?

Question 71

A baby weighs 9 pounds at birth and 30 pounds at age 3.Use a graphing calculator to graph the resulting equation and determine how much the child will weight at age 12.

Question 72

A California homeowner with a 30-year fixed rate mortgage pays $170,000 after 5 years and $266,000 after 9 years.Use a graphing calculator to graph the resulting equation and determine how much the homeowner will have paid when the mortgage is paid off in 30 years.

Question 73

A deep sea diver has spent a week in a submerged research facility at 2000 feet below sea level.He is now ready to move to a deeper facility at 3500 feet below sea level.He descends at the rate of 50 feet per minute.Write an equation that shows this relationship,and determine when the diver will reach 3500 feet below sea level.

Question 74

Show that the points A(0,0),B(0,3),C(8,5),and D(12,3)are the vertices of a trapezoid.(A trapezoid is a four-sided figure with exactly two sides parallel.)

Question 75

The size of a human fetus more than 12 weeks old can be estimated by the formula L = 1.53t - 6.7,where L is in centimeters and t is in weeks.An obstetrician uses the length of a fetus,measured in an ultrasound,to determine the approximate age of the fetus and establish a due date for the mother.The formula must be rewritten to result in an age t,given a fetal length L.Use a graphing calculator to graph the resulting equation and verify the y-intercept.

Question 76

The average weight of newborn blue whales is 3 tons.By the time they are 7 months old the average weight of these whales is 23 tons.Draw a line showing the relationship between weight (in tons)and age (in months)of blue whales.Find and interpret the slope.

Question 77

Graph the general linear form of the child dosage equation whose slope-intercept form is

Question 78

A delicatessen owner starts her business with debts of $100,000.After operating for 5 years she has average profits of $40,000 per year.Use a graphing calculator to graph the resulting equation and determine when the business will have accumulated $300,000 in profit.

Question 79

A botanist collected data from an experiment on the amount of oxygen released by a plant given different amounts of an experimental fertilizer.He graphs the data with grams of fertilizer given in a day on the x-axis and milliliters of oxygen produced in a day on the y-axis.His data points are: (1,0.02),(3,0.02),(5,0.02),
(7,0.02).Find an equation for the line which fits this data and interpret its meaning.

Question 80

A coordinate map of a zoo shows the outdoor aviary at (2,4)and the snack bar at (2,8).What is an equation for the line between these two locations?