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Word Problems

Browse Middle School Graphing Equations
Stars indicate particularly interesting answers or good places to begin browsing.

Selected answers to common questions:
    Direct and indirect variation.
    Slope, slope-intercept, standard form.

Equation of a Line Parallel to an Axis [06/19/2003]
How can I get the equation of a line if the line passes through a point and is parallel to the x- or y-axis?

Equations of a Line given Two Points [8/31/1996]
How do you find the equation of a line going through two points if you only know the two points?

Geometric Objects and Properties using Algebra [06/29/1998]
Why does y = mx+b, and what does it mean?

Graphing a Parabola [12/15/1994]
How do I graph a parabola (without a calculator)?

Graphing Coordinates [1/15/1997]
How can you tell if you have a straight line just by looking at the numbers?

Line of Best Fit [07/08/2003]
I am looking for help in how to manually find the slope and intercept of this problem.

Nomographs [06/12/2003]
What are nomographs used for? How does one use them? Are they still in use? and last but not least, How are they constructed?

No Solution, Infinite Solutions [01/03/2002]
Solve: 8(2x-3) = 4(4x-8); -3(x-3) is greater than or equal to 5-3x.

Please graph and send the solution for: [5/23/1995]
(x^2 + y^2)/2 = 0

Slope Angle [06/17/2003]
What units do we use to refer to slope?

Undefined Slope and Zero Slope [04/11/1997]
What is the difference between an undefined slope and a slope of zero?

Absolute Value Graphs [11/16/2002]
Graphing inequalities: finding an equation, graphing it, and finding its vertices.

Changing Equations To Slope-Intercept Form [07/17/1998]
Can you explain how to change equations into slope-intercept form? For example, 12(2x-1) - 5(3y+2) = 8?

Deriving the Quadratic Formula [10/15/1998]
How do you derive the quadratic formula from ax^2 + bx + c = 0?

Direct and Indirect Variation [07/09/1998]
Can you explain the difference between direct and indirect variation? How would you interpret them in a word problem?

Drawing a Line, Given the Slope and One Point [05/23/2002]
How do I draw a line on a graph when I know the slope and the location of only one point on the line?

Drawing Equations on the Number Line [05/09/2002]
How can I draw an equation like 2 - (-5) = 7 on a number line?

Finding the Equation of a Line [01/08/1997]
Given either a point and a slope or two points, how do you find the equation of a line in both point-slope and standard form?

Finding the Equation of a Line [2/2/1996]
Find the value of k and m if the straight line y = kx + m passes through the point (-2,5) and has a gradient of 4.

Finding the Table's Diameter [05/05/2001]
A circular table is pushed into the corner of a room so that it touches both walls. On the edge of the table is a scratch 8" from one wall and 9" from the other wall. What is the diameter of the table?

Finding y-intercepts [6/12/1996]
I'm having a problem with finding and graphing y-intercepts of linear equations.

Graphing Inequalities [10/16/1998]
Could you explain to me how to graph inequalities that use variables, such as x < 2? Where do you shade? Is the line dotted or solid?

Graphing Inequalities [06/05/2003]
How do you graph y + 4x is less than 20 ?

Graphing Intercepts [11/06/1997]
How would I find the intercept for a problem such as 3x-2y = 12?

Graphing Linear Equations [12/26/2001]
Give the intercepts of 7x - 2y = 2.

Graphing Systems of Equations [06/01/1998]
How do you solve this system of equations by graphing: 3x + 2y = 5 and - 3x - 2y = 10?

Graphing without the Y [01/28/2004]
I'm trying to graph the inequality x > -5, but without a y, how can I graph it?

Graphing y = mx + b [01/20/1997]
After you get 3 x+ 2y = 5 into y = mx + b form, how do you graph it?

Height and Weight [10/30/1996]
How do you find a formula that predicts a person's weight when all you know is his/her height?

Hidden in x-y Plane Sight [11/29/2011]
A student wonders why x = 4 represents a vertical line. Using several two-variable examples in standard form, Doctor Ian builds up an explanation — and reveals a hidden implication: that single-variable equation actually contains a second variable with coefficient zero.

How to Draw Linear Equations [06/07/1999]
How would I draw the line y = (2/3)x + 5?

Inequalities on a Number Line [05/07/2003]
How do you graph inequalities on a number line?

Infinity and Inequalities [06/05/2002]
I'm supposed to use positive and negative infinity to solve problems like 2x - 3 < 7.

Intercept Equation [10/07/1998]
I found a plane using the intercepts (4,0,0), (0,-5,0), and (0,0,3). Now I want an equation for those points using Ax + By + Cz = D.

Introduction to Quadrants in the Coordinate Plane [02/05/2004]
What is a quadrant? How do you find it? I had to identify 9 ordered pairs on a graph. Now I need to also name the quadrant each one is in.

Is It Really Possible to Draw a Graph? [02/01/2007]
Since graphs are collections of points, and points have no dimensions (depth, length, height), we can't really draw a graph. All we can do is make a "representative graph". Is that right?

Line of Best Fit [8/1/1996]
Are a best-fit line, a line of best fit, and a fitted line synonymous?

Multiplying or Dividing by a Negative Number [04/08/1999]
When x(x-4) is less than 0...

Non-parallel Glide Reflections [10/21/1998]
A glide reflection consists of a line reflection and a translation parallel to the reflection. What if the translation is not parallel to the reflection?

Order of Quadrant Numbers [10/21/2002]
Why are quadrants numbered that way?

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