Slope of a Line

The slope of a line which is represented by the variable “m” is front and center when it comes to understanding graphs of lines (linear equations).  What is the slope?  It’s simple it’s just the measurement of the angle of the line.  Lines that rise from left to right (like the image below) have positive slopes.  Lines that fall from left have a negative slope.  The greater the value of the slope the “steeper” the angle of the line.  All right now onto the definition of the slope (m) this is really important so pay close attention.  The slope is equal to the “rise over the run”.  But what does this mean? The rise is how much a line goes up ( measured along the y-axis) and the run is the measure of how much the line goes sideways (measured along the x-axis).  The steps below will show you how to calculate the slope but I  want to stress a very important point about the most common slope mistake-   I will use the example below to illustrate my point:

Do you see that I used the x and y values from the point ( 1, 6) first when plugging in the numbers into the slope equation?  This is not a little detail- you must pick one point and plug in it’s information first, you can’t mix the data.  For example lets say I was calculating the slope in the following manner   m=( 6 – 1 )/ (2 – 1 ) do you see how I reversed the order in the denominator?  that would cause your answer to be wrong.  So,  pick a point and plug in it’s respective coordinates first….really practice calculating the slope it comes up everywhere in algebra.  

 

 

some key topics that involve finding the slope of a line:

* linear equations
* writing linear equations
* slope-intercept formula
* point-slope formula
* systems
* SAT and ACT exams
* college prep math and science courses


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