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Algebra sloping

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3 Answers

to find a slope using two points on a line, use this formula:   (y2 - y1)/(x2 - x1)

let's say point (3, 9) is point 1, so x1 = 3, y1 = 9

so point (-2, -3) is point 2, so x2 = -2, y2 = -3

so using the formula, we have   (-3 - 9)/(-2 - 3) ---> -12/-5 so slope is 12/5

Yes. A slope does exist. Slope is just "Rise over run".

(y1 - y2) / (x1 - x2) = m

This can also be expressed as: m = Δy / Δx    (slope equals Delta y over Delta x [Delta is commonly used to represent "the change in".])

So... plug in the values:
(9 - (-3)) / (3 - (-2)) = m
(9 + 3) / (3 + 2) = m

m = 12 / 5

Hopefully that's somewhat clear. I'll try to clarify further if not.

Begin with reviewing your understanding of what is the slope of a line?  Think of places in real life where the word slope is used,  for example a ski slope.  What does that look like?  When you translate that into math what you are looking for is the steepness of a line. 

For beginners I would suggest graphing the two points.  

Draw the line between them,  is the line horizontal?  If so then it has no steepness therefore the slope is zero.

Is the line vertical?  If so then you do not have a slope,  in fact the only way a line does not have a slope is if it is vertical.  You can also discover this by looking at your points.  When a line is vertical what is the x value?  What is the y value?  If you x value is the same for both points you will have a vertical line, therefore no slope exists.

 

Once you have determined whether the line is vertical or horizontal and it is not.  You can then use  the slope formula which helps you find the change in y and the change in x.  Delta y and delta x is the mathematical way to express this.

To find a change you will subtract of y in the first point from y in the second point.  That is your numerator,  then you will subtract the values of x in the first point from x in the second point,  that is your denominator.  Write the slope as the ratio with your anwers to the above.

 

Example  Point 1  (3, 9) and Point 2 (-2, -3)

Subtract the y values (-3 - 9)  this = -12

subtract the x values (-2 - 3)  this = -5

your slope is -12/-5.