Lesson Objectives: Students will look at real-life applications of slope, including roofs, roads, handicap ramps, funiculars, cable cars, mountains for skiing, downhill cycling, and snowboarding/dirtboarding, roller coasters, skate ramps, and BMX jumps.

Slope is calculated by finding the ratio of the “vertical change” to the “horizontal change” between (any) two distinct points on a line. Sometimes the ratio is expressed as a quotient (“rise over run”), giving the same number for every two distinct points on the same line.

Slope measures the rate of change in the dependent variable as the independent variable changes. Mathematicians and economists often use the Greek capital letter D or D as the symbol for change. Slope shows the change in y or the change on the vertical axis versus the change in x or the change on the horizontal axis.

Slope is a measure of steepness….Some real life examples of slope include:

1. in building roads one must figure out how steep the road will be.
2. skiers/snowboarders need to consider the slopes of hills in order to judge the dangers, speeds, etc.
3. when constructing wheelchair ramps, slope is a major consideration.

Slope is change in y over change in x. In the real world, this can be used to find things like speed from a graph of the position of something, which is the change in speed over a given time interval.

1 Expert Answer The sign of the slope tells you if a line is ascending or desc⁄ending. A positive slope tells you that a line travels up and to the “right” like this, ⁄, (uphill from left to right). A negatively sloping line travels the opposite way, like this, / (downhill from left to right).

We have been learning about slope in class. The Slope Intercept form of an equation is very important for helping us graph and understand linear situations. By definition slope is the steepness of a line. …

In the equation of a straight line (when the equation is written as “y = mx + b”), the slope is the number “m” that is multiplied on the x, and “b” is the y-intercept (that is, the point where the line crosses the vertical y-axis). This useful form of the line equation is sensibly named the “slope-intercept form”.

Pattern for Sign of Slope If the line is sloping upward from left to right, so the slope is positive (+). If the line is sloping downward from left to right, so the slope is negative (-).

The slope of a line can be positive, negative, zero, or undefined. A horizontal line has slope zero since it does not rise vertically (i.e. y1 − y2 = 0), while a vertical line has undefined slope since it does not run horizontally (i.e. x1 − x2 = 0). because division by zero is an undefined operation.

The equation for a zero slope line is one where the X value may vary but the Y value will always be constant. An equation for a zero slope line will be y = b, where the line’s slope is 0 (m = 0).

A zero slope is just the slope of a horizontal line! The y-coordinate never changes no matter what the x-coordinate is! In this tutorial, learn about the meaning of zero slope.