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.