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Linear Equations and Graphs: Solving Problems Involving Slope, Intercepts, and Systems - P, Exams of Mathematics

Augusta Technical CollegeMathematics
Prof. Nancy Molik

A collection of linear equation problems from a spring 2009 exam for the course mat 1101. Students are required to simplify equations, find intercepts, determine slopes, and graph lines. Problems include finding the equations of lines passing through specific points and having a given slope, as well as solving systems of linear equations.

Typology: Exams

Pre 2010

Uploaded on 08/18/2009

koofers-user-l51-1
koofers-user-l51-1 🇺🇸

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bg1
+−=
−=
3
3
1
42
xy
xy
Test 2 MAT 1101 Spring 2009 Name ________________________
Simplify all answers and show your work! You may use MathGV as a tool.
1. In the linear equation 3x + 5y = 15, what is the x-intercept? ___________ y-intercept? ___________
2. In the equation 4x – 7y = 12, what is the value of the slope? ____________
3. Lines that are parallel have the same ____________.
4. In the equation Ax + By = C, what is the value of the slope? ____________
Find the equations of the lines with the given properties:
5. Passing through points 6. Passing through (-2, 3) and
(2, 3) and (-1, 6). having a slope of
3
5
−.
7. Solve for x: 2(x + 5) = 3x – 4(x + 1) 8. If f(x) =
9
27
+
x, find the inverse (f -1(x)).
9. Graph the following system of equations. 10. Solve the system of equations:
=+
=−
73
825
yx
yx
and find the point of intersection.
Determine if the following pairs of lines cross in one point, are parallel, or are the same line.
11.
=+
=+
39153
135
yx
yx 12.
=−
=−
2
277
yx
yx 13.
=−
=+
29106
1253
yx
yx
pf2

Partial preview of the text

Download Linear Equations and Graphs: Solving Problems Involving Slope, Intercepts, and Systems - P and more Exams Mathematics in PDF only on Docsity!

y x

y x

Test 2 MAT 1101 Spring 2009 Name ________________________

Simplify all answers and show your work! You may use MathGV as a tool.

  1. In the linear equation 3x + 5y = 15, what is the x-intercept? ___________ y-intercept? ___________
  2. In the equation 4x – 7y = 12, what is the value of the slope? ____________
  3. Lines that are parallel have the same ____________.
  4. In the equation Ax + By = C, what is the value of the slope? ____________

Find the equations of the lines with the given properties:

  1. Passing through points 6. Passing through (-2, 3) and

(2, 3) and (-1, 6). having a slope of 3

  1. Solve for x: 2(x + 5) = 3x – 4(x + 1) 8. If f(x) = 9

7 x + 2 , find the inverse (f -1(x)).

  1. Graph the following system of equations. 10. Solve the system of equations: 

x y

x y

and find the point of intersection.

Determine if the following pairs of lines cross in one point, are parallel, or are the same line.

x y

x y

x y

x y

x y

x y

  1. A storage tank contains 540 gallons. Gasoline is then pumped out of the storage tank at a rate of 12 gallons per minute until the tank is empty. Let G(x) represent the amount of gasoline left in the tank after “x” minutes.

a) What is the rate of change? b) How much gasoline is in c) Find the linear equation G(x). the tank when x = 0?

d) How much gasoline is in the tank after 10 minutes? e) How many minutes does it tank to empty the tank?

  1. Ammonium chloride salt must be a certain temperature to dissolve in a given amount of water. At 10o Celsius, 33 grams of water can be dissolved; and at 40o^ Celsius, 48 grams of water can be dissolved. Let g(x) represent the number of grams of ammonium chloride salt that can be dissolved at xo^ Celsius.

a) What is average rate of change b) Find the equation g(x). in grams per degree Celsius?

c) How many grams can be d) What would the temperature need to be to dissolve dissolved at 0o^ Celsius? 100 grams of ammonium chloride in the water?

  1. The number of calories burned by cycling for “x” hours can be calculated by the formula C(x) = 794x.

a) How many calories are burned b) Lance Armstrong cycles 6 hours a day. How per hour of cycling? many calories does he burn each day by cycling?

c) If 1 pound of weight is 3500 calories, how long does one have to cycle to exercise off 1 pound?

  1. Kim bought $0.42 stamps for letters and $0.27 stamps for postcards. She bought a total of 170 stamps for $53.40. How many stamps for postcards did she buy?