what is an easy way to find slope

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embizze | High School Teacher | (Level 1) Educator Emeritus

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If you were to learn only one way to find slope, you would probably want to choose the most general method.

You will need to find two points. You might be given the two points (perhaps as coordinate pairs, or in a table, or you might read them from a graph.) Then the slope is `("changein"y)/("changein"x)` : given two points `(x_1,y_1),(x_2,y_2),m=(y_2-y_1)/(x_2-x_1)` .

For example, if the points are (2,5) and (3,7) the slope is `m=(7-5)/(3-2)=2/1` or m=2. Did it matter which point we chose first? Not at all: `m=(5-7)/(2-3)=(-2)/(-1)=2/1=2` .

The two most common errors I have encountered are (1) Putting the difference of the x's in the numerator and (2) going right to left in the numerator, then going left to right in the denominator.

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You don't want to stop there. Sometimes you are given the equation of a line. You really don't want to find two points from that line to calculate slope every time.

If given a line in slope-intercept form y=mx+b the slope is m.

If given a line in point-slope form `y-y_1=m(x-x_1)` the slope is m.

If given a line in standard form Ax+By=C the slope is `m=-A/B`

Parallel lines have the same slope while perpendicular lines have opposite/reciprocal slopes.

From a graph you can find `m="rise"/"run"` where the rise is the change in y, and the run is the change in x.

Finally, if you are given a word problem, look for a rate. Slope is a constant rate of change: e.g. If you are told that each game of bowling costs $2, an equation giving the cost of a bowling trip will include a term like 2x where x is the number of games bowled, and 2 is the slope of the line.

If you truly understand what slope is, you will find it much easier to compute it from given information.

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