Slope

Have you ever been skiing or seen it on television?• What is the

difference between the beginner’s trail (bunny slope) and the expert’s trail (black diamond slope)?

Trail Map

Slope

• In skiing, slope refers to a slanted mountainside.

• The steeper the slope is, the higher its difficulty rating will be (green - double black diamond)

Slope in Math

• In math, slope defines the slant of a line.

• The larger the absolute value of a slope is, the steeper, or more vertical, the line will be.

Slope

Linear equations have constant slope. For a line on the coordinate plane, slope is the ratio….

“Rise over Run”

• Rise is the number of units moved up or down. (y- axis)

• Run is the number of units moved left to right (x- axis)

• Slope can be positive, negative, zero, or undefined.

Slopes Defined

Positive Negative Undefined Zero

Can I find a slope without graphing?

If you know any two points on a line, or two solutions of a linear equation, you can find the slope of a line without graphing.The slope of a line through the points (x1, y1) and (x2, y2) is as follows:

Variable Rate of Change

• Nonlinear equations have variable rates of change. This means that the rate of change is different between different values. This is shown in a graph by a curved line:

Constant Rate of Change

• Linear equations have constant rates of change. This means that the rate of change is always the same. This is shown in a graph by a straight line.