Calculating Slope of a Line What you should have remembered from Gr. 9! See…your teachers told you you’d see it again…..and??? They were correct!!

The slope of a line describes the following: The steepness of a line The vertical change relative to the horizontal change The change in the y-direction relative to the change in the x-direction x y Horizontal change (run) ( ∆ x) Vertical change (rise) ( ∆ y)

The slope of a linear equation (straight line) is the same everywhere. A line with positive slope rises from left to right. A line with negative slope falls from left to right.

x y Use points (0,1) and (2,3) to calculate the slope slope = ∆ y ∆ x = y 2 – y 1 x 2 – x 1

Very steep lines have large slopes, while relatively flat lines have small slopes. More facts: x y Question: Which of the three lines above have the largest slope? Answer: The blue line!

Line of Best Fit When calculating slope of a data set, your data may not be perfectly linear. You must draw a line of best fit! Draw a line through the data points.

Line of Best Fit Your line should pass through as many points as possible and follow the general trend of the coordinates. To calculate slope, pick two coordinates that are far apart and touching/close to your line of best fit. Slope= ∆ y ∆x∆x =y 2 – y 1 x 2 – x 1 =2.4 – – 2.0 = = = -.69 (x 1, y 1 ) (x 2, y 2 )

Animation (regression)

The slope of a line can be calculated from : a table a graph two coordinate points on the line using the formula : 1 2 3