Basic Algebra/Lines (Linear Functions)/Slope of a Line

Vocabulary

Slope of a line: A number determined by any two points on the line that describes how steep the line is. A vertical line,having absolute steepness, has a slope that is undefined. A horizontal line, having no steepness, has a slope of 0. Lines that rise from left to right have a positive slope. Lines that fall from left to right have a negative slope. So a diagonal line to the right ( / ) would have a positive slope. A diagonal line to the left ( \ ) would have a negative slope. A vertical line ( | )has an undefined slope and a horizontal line ( ---- ) has a slope of 0.

Lesson

To understand the Cartesian Coordinate graph and how it works, you must know how number lines work. A number line is a line of numbers that streches infinitely on both sides. The Negative numbers extend infinitely to the left and the Positive numbers go infinitely to the right. Zero sits right smack in the dead center of the line however long it might be. A cartesian coordinate graph is just two infinite number lines one vertical(the X-axis) and one horizontal(the Y-axis) on top of each other forming a cross with 0 as the center point or Origin as it is called. The graph is also divided into 4 quadrants. these are numbered with Roman numerals.

http://commons.wikimedia.org/wiki/Image:2D_Cartesian_Coordinates.svg

However, for understandability's sake, this graph is usually shortened to -6 and + 6 on both the X and Y axis. Also, however, this graph is also ugly and not very user friendly. (Gridboard)

Now, how to determine the slope of a line: Let's pretend that we are baking giant chocolate cookies for a bake sale. Right before you start your Bake-O-Rama, You make three of them. You figure you can make two an hour. You also take inventory every hour like this:

                         Hours Cookies
                          0      (2x0)+3=3
                          1      (2x1)+3=5
                          2      (2x2)+3=7

Example Problems

slope (m) = ${\frac {y_{2}-y_{1}}{x_{2}-x_{1}}}$

Using the points in the diagram above, x₁ and y₁ are both 2 and x₂ is 6 and y₂ is 4. So we substitute each value into the slope equation.

Practice Games

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