Day 48 – November 3

Algebra: Chapter 7, Lesson 4, page 318

Slope of a Line

The slope of a line is the tilt or slant. The slope is defined as the letter ${\displaystyle m}$ and ${\displaystyle m=\frac{rise}{run}}$, where the ${\displaystyle rise}$ is the change in the y-coordinate and the ${\displaystyle run}$ is the change in the x-coordinate. This definition works great when you have 2 points on graph paper. You can just count the squares for the rise and the run. It doesn’t matter too, which point you start with.

Remember, slope is positive if the line is going from lower left to upper right. The slope is negative if its coming from upper left to lower right.

A slope of 0 is a horizontal line and a line with NO SLOPE is a vertical line.

Another definition of slope, given 2 point and NO GRAPH PAPER is:

${\displaystyle m=\frac{y_2-y_1}{x_2-x_1}}$, where ${\displaystyle (x_1,y_1)}$ and ${\displaystyle (x_2,y_2)}$ are 2 points on the line.

For example, for the points (2, 3) and  (-4, 2), the slope is:

${\displaystyle m=\frac{2–(-3)}{-4–2}=\frac{5}{-6}=-\left(\frac{5}{6}\right)}$

Purplemath has this link as well.