Graphing Linear Equations 3.4

3.4 Slope and Applications
a. Given the coordinates of two points on a line, find the slope of the line, if it exists.
b. Find the slope, or rate of change, in an applied problem involving slope.
c. Find the slope of a line from an equation.

Objective a
Given the coordinates of two points on a line, find the slope of the line, if it exists.







Example A Graph the line containing the points (-4, 5) and (4, -1)
and find the slope.





Objective b
Find the slope, or rate of change, in an applied problem involving slope.

Applications of Slope
Some applications use slope to measure the steepness. For examples, numbers like 2%, 3%, and 6% are often used to represent the grade of a road, a measure of a road’s steepness. That is, a 3% grade means that for every horizontal distance of 100 ft, the road rises or drops 3 ft.

Example B
Find the slope (or grade) of the treadmill.


Objective c
Find the slope of a line from an equation.

It is possible to find the slope of a line from its equation.



Example C



Example D



Example E Find the slope of the line y = 3



Example F Find the slope of the line x = 2