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Math Problem Solving: Finding Equations of Lines, Circles, and Solving Systems - Prof. Her, Exams of Algebra

Abraham Baldwin Agricultural College (ABAC)Algebra
Prof. Herbert E. Henderson

A collection of math problems that require finding equations of lines given their properties, determining the midpoint of a line segment, deciding if points form a right triangle, and solving systems of linear equations. It also includes problems on finding the distance between points and determining if points are endpoints of a diameter of a circle.

Typology: Exams

Pre 2010

Uploaded on 08/16/2009

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SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Solve the problem.
1)
Bob wants to fence in a rectangular garden in his yard. He has
82
feet of fencing to work
with and wants to use it all. If the garden is to be x feet wide, express the area of the garden
as a function of x.
1)
Find an equation for the line, in the indicated form, with the given properties.
2)
Containing the points (
8
,
5
) and (
4
,
8
); slope
intercept form
2)
Find the slope
-
intercept form of the equation of the line with the given properties.
3)
Slope
=
6
; y
intercept
=
8
3)
Find the slope and y
-
intercept of the line.
4)
3
x
5
y
=
1
4)
Find an equation for the line with the given properties.
5)
Parallel to the line
4
x
3
y
=
29
; containing the point (
2
,
2
)
5)
6)
Perpendicular to the line y
=
3
x
2
; containing the point (
4
,
4
)
6)
1
pf3
pf4

Partial preview of the text

Download Math Problem Solving: Finding Equations of Lines, Circles, and Solving Systems - Prof. Her and more Exams Algebra in PDF only on Docsity!

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Solve the problem.

  1. Bob wants to fence in a rectangular garden in his yard. He has 82 feet of fencing to work

with and wants to use it all. If the garden is to be x feet wide, express the area of the garden

as a function of x.

Find an equation for the line, in the indicated form, with the given properties.

  1. Containing the points (- 8 , - 5 ) and (- 4 , - 8 ); slope-intercept form 2)

Find the slope-intercept form of the equation of the line with the given properties.

  1. Slope = 6 ; y-intercept = 8 3)

Find the slope and y-intercept of the line.

  1. 3 x + 5 y = 1 4)

Find an equation for the line with the given properties.

  1. Parallel to the line 4 x + 3 y = 29 ; containing the point ( 2 , 2 ) 5)

  2. Perpendicular to the line y = 3 x + 2 ; containing the point (- 4 , 4 ) 6)

Use a graphing utility to find the equation of the line of best fit. Round to two decimal places, if necessary.

x 1 3 5 7 9

y 143 116 100 98 90

Solve the system.

2x + 10 y = - 64

11x + 2y = 72

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Solve the system.

x - 4y = - 10

2x - 8y = - 17

A) dependent (many solutions) B) (2, 3)

C) (2, 4) D) inconsistent (no solution)

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Find the distance d(P 1

, P

) between the points P 1

and P 2

x -8 -6 -4 -2 2 4 6 8

y

8

6

4

2

x -8 -6 -4 -2 2 4 6 8

y

8

6

4

2

Decide whether or not the points are the vertices of a right triangle.

Find the midpoint of the line segment joining the points P 1

and P 2

12) P

= (-0.1, - 0.2); P

Answer Key

Testname: M1111 FALL08 TEST

  1. A(x) = 41x - x
  1. y = -

x - 11

  1. y = 6 x
  1. slope =

; y-intercept =

  1. 4 x + 3 y = 14

  2. y = -

x

  1. y = - 6.2x + 140.

  2. x = 8 , y = - 8

9) D

  1. Yes

  1. 7.5 mph

  2. 16 lb

  3. y = -

x

3, where x is any real number

  1. (x - 6)
  • (y - 5)
  1. (x - 1)
  • (y - 1)