Jan 062012
Understand the slope of a line and how it can be used to solve various problems on the SAT Exam is a crucial concept to master.
•The slope, or steepness, of a line is a concept that will appear often in SAT problems. To find the slope, pick any two points on the line and apply the Slope Formula.
–Slope = Vertical Change / Horizontal Change = y2-y1/x2-x1
–Example: Find the slope of the line that contains the points (3, 4) and (1, 2).
Slope = 4-2/3-1 = 2/2 = 1
•A line that rises from left to right has a positive slope, while a line that falls from left to right has a negative slope.
–A horizontal line has a slope of zero, while a vertical line has a slope that is not defined.
•Note: Any two points on a given line can be used to determine the slope of the overall line.
•Remember that parallel lines have equal slopes.
•Also remember that perpendicular lines have slopes that are negative reciprocals of one another.
–Example: Two lines whose slopes are 2 and –½ are perpendicular to each other since their slopes are the negative reciprocals of each other.