Chapter 11: Coordinate Graphing 141CHECK POINT
Graph each equation by intercept-intercept.- x y 10
12.^6212 xy - 23 9xy
14. x^28 y
15.^6218 xy
The other quick graphing method uses the y-intercept and a pattern we notice in lines, called the
slope of the line. The slope of a line is a measurement of the rate at which the line rises or falls.
A rising line has a positive slope, and a falling line has a negative slope. A horizontal line has a
slope of zero, and a vertical line has an undefined slope. A line with a slope of 4 is steeper than
a line with a slope of 3. A line with a slope of -3 falls more steeply than a line with a slope of -1.
DEFINITION
The slope of a line is a number that compares the rise or fall of a line to its horizontal
movement.The slope of a line is found by counting from one point on the line to another and making a ratio
of the up or down motion to the left or right motion. The up or down motion is called the rise,
and the left or right motion is called the run. So the slope is riserun.
The traditional symbol for the slope is m. If you know two points on the line, you can find the
rise by subtracting the y-coordinates and the run by subtracting the x-coordinates. If the points
are (x 1 ,y 1 ) and (x 2 ,y 2 ), then
m riserun yyxx^21
21
5522.
Because you find the slope by subtracting the y’s to find the rise and subtracting the x’s to f ind
the run, the formula for the slope can be written as m yyxx^21
21