Slope
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Key Questions

Answer:
Slope is the change in the y values divided by the change in the x values
Explanation:
#"slope"="rate of change in y"/"rate of change in x" ="rise"/"run"# #(color(blue)(x_1),color(blue)(y_1))# #(color(red)(x_2),color(red)(y_2))# #color(green)m =(color(red)(y_2)color(blue)(y_1))/(color(red)(x_2)color(blue)(x_1))# Is is often expressed as rise over run.

The slope is a number that tells you how much y changes when x changes.
For example: a slope of 5 means that for each change in x of 1 unit (for example between 6 and 7) the correspondig y changes of 5 units.
This is for a positive slope, so that your value of y is getting...bigger!!!The negative slope is the opposite, it tells you of how much y decreases for each increas of 1 unit in x.
A slope of 5 tells you that the value of y decreases of 5 units in the 1 unit interval of x:
As you may guess the slope is a measure of the "inclination" of your line!!!
Try to guess what a slope of zero means!!!!!!

Use the slope formula (
#m = (y_2  y_1)/(x_2  x_1)# ) to calculate the slope given two points#(x_1, y_1)# and#(x_2, y_2)# .Here is an example of finding the slope, given two points (2,3) and (4,5).
#(2, 3) = (x_1, y_1)#
#(4, 5) = (x_2, y_2)# #m = (y_2  y_1)/(x_2  x_1)# #m = (5  3)/(4  (2))# #m = (5  3)/(4 + 2)# #m = (8)/(6)# #m =4/3# The slope of of (2,3) and (4,5) is
#4/3# 
Nuzhat has already discussed how you can find the slope of a line from two points that lie on the line. I'll discuss two other methods of finding the slope from a graph.
1. From the angle made with the xaxis
Since the slope of a line is basically the ratio of the ycomponent of the line to its xcomponent,
The slope of a line can be found out by taking tangent of the angle between the given line and the xaxis.
Consider the following figure:
In this case, the angle between the xaxis and the line is
#theta# .Therefore,
Slope of the given line =#tantheta# Note: Angles in the counterclockwise direction are taken as positive, and those in the clockwise direction are taken as negative.
For example, if the angle between the xaxis and the given line is
#30^o# ,Slope of the given line =
#tan30=1/sqrt3# 2. From the equation of the line
The slope of a line can also be determined from its equation. The standard form of the equation of a line is:
#Ax^2+By+C=0# where
#A,B and C# are some constants.First, the equation of the line must be written in the standard form.
Then, the slope of the line =
#A/B# For example, let the equation of the given line be
#x^2+3=2y# .Rewriting in the standard form, we get:
#x^22y+3=0#
and we can see that:
#A=1#
#B=2#
#C=3# Therefore, the slope of the line
#=A/B=(1)/(2)=1/2# 
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Questions
Graphs of Linear Equations and Functions

1Graphs in the Coordinate Plane

2Graphs of Linear Equations

3Horizontal and Vertical Line Graphs

4Applications of Linear Graphs

5Intercepts by Substitution

6Intercepts and the CoverUp Method

7Slope

8Rates of Change

9SlopeIntercept Form

10Graphs Using SlopeIntercept Form

11Direct Variation

12Applications Using Direct Variation

13Function Notation and Linear Functions

14Graphs of Linear Functions

15Problem Solving with Linear Graphs