A Guide to the GRE/Coordinates and Graphing

= Coordinates & Graphing =

Rules
In a standard coordinate plane, points are given locations of (x, y), where “x” is the horizontal coordinate and y is the vertical coordinate.

The x coordinate is also called the “abscissa”, while the y coordinate is called the “ordinate.”

The slope of a line graphed on the coordinate plane is equal to rise divided by run. If a line is expressed by an equation, the slope of the line is the number in front of the x when the equation is in the form y = ax + b.

For example, if the equation for a line is y = 2x + 1, the slope is 2 and the y intercept is 1. If the line is in the form y - +2x = 1, rearrange it so that it is in the above format - y = mx + b.

To determine when a line crosses the x or y axis, set x or y equal to zero.

For example, a line with the equation y = 6x - 5 crosses the y axis at (0, -5).

Practice
1. The equation for a line is 2y - 4x - 5 = 0. What is the slope of the line?

2. What is the slope of a line which passes through points (3, -2) and (6,3)?

Comments
What is the equation for the line above?

Answers to Practice Questions
1. 2

When a line is in the form y = mx + b, m is the slope of the line and b is the y intercept. If a line is not in this format, it should be converted into this format.

2y - 4x - 5 = 0		Take the initial equation.

2y - 4x = 5		Add 5 to both sides.

2y = 4x + 5		Add 4x to both sides.

y = 2x +		Divide both sides by 2. The slope of the line is 2.

2.

The slope of this line is rise over run, or This equals or

3. y = 3x + 1

When a line is in the form y = mx + b, m is the slope of the line and b is the y intercept.

The line crosses the y axis at (0,1) and thus its intercept is 1. It passes through the point (1,4) after passing through (0,1) meaning it has a rise of 3 for every unit of run. Thus, the slope of the line is 3 and its equation is y = 3x + 1.