How to Find the Slope of an Equation
Use slope to determine how steep, and in what direction (upward or downward), a line goes., Find the number in front of the x, usually written as "m," to determine slope., Reorganize the equation so one variable is isolated if the slope isn't...
Step-by-Step Guide
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Step 1: Use slope to determine how steep
Finding the slope of a line is easy, as long as you have or can setup a linear equation.
This method works if and only if:
There are no exponents on the variables There are only two variables, neither of which are fractions (for example, you would not have 1x{\displaystyle {\frac {1}{x}}} The equation can be simplified to the form y=mx+b{\displaystyle y=mx+b}, where m and b are constants (numbers like 3, 10,
-12, 43,35{\displaystyle {\frac {4}{3}},{\frac {3}{5}}}). -
Step 2: and in what direction (upward or downward)
If your equation is already in the right form, y=mx+b{\displaystyle y=mx+b}, then simply pick the number in the "m" position (but if there is no number written in front of x then the slope is 1).
That is your slope! Note that this number, m, is always multiplied by the variable, in this case an "x." Check the following examples: y=2x+6{\displaystyle y=2x+6} Slope = 2 y=2−x{\displaystyle y=2-x} Slope =
-1 y=38x−10{\displaystyle y={\frac {3}{8}}x-10} Slope = 38{\displaystyle {\frac {3}{8}}} , You can add, subtract, multiply, and more to isolate a variable, usually the "y." Just remember that, whatever you do to one side of the equal sign (like add 3) you must do to the other side as well.
Your final goal is an equation similar to y=mx+b{\displaystyle y=mx+b}.
For example:
Find the slope of 2y−3=8x+7{\displaystyle 2y-3=8x+7} Set to the form y=mx+b{\displaystyle y=mx+b}: 2y−3+3=8x+7+3{\displaystyle 2y-3+3=8x+7+3} 2y=8x+10{\displaystyle 2y=8x+10} 2y2=8x+102{\displaystyle {\frac {2y}{2}}={\frac {8x+10}{2}}} y=4x+5{\displaystyle y=4x+5} Find the slope:
Slope = M = 4 -
Step 3: a line goes.
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Step 4: Find the number in front of the x
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Step 5: usually written as "m
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Step 6: " to determine slope.
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Step 7: Reorganize the equation so one variable is isolated if the slope isn't apparent.
Detailed Guide
Finding the slope of a line is easy, as long as you have or can setup a linear equation.
This method works if and only if:
There are no exponents on the variables There are only two variables, neither of which are fractions (for example, you would not have 1x{\displaystyle {\frac {1}{x}}} The equation can be simplified to the form y=mx+b{\displaystyle y=mx+b}, where m and b are constants (numbers like 3, 10,
-12, 43,35{\displaystyle {\frac {4}{3}},{\frac {3}{5}}}).
If your equation is already in the right form, y=mx+b{\displaystyle y=mx+b}, then simply pick the number in the "m" position (but if there is no number written in front of x then the slope is 1).
That is your slope! Note that this number, m, is always multiplied by the variable, in this case an "x." Check the following examples: y=2x+6{\displaystyle y=2x+6} Slope = 2 y=2−x{\displaystyle y=2-x} Slope =
-1 y=38x−10{\displaystyle y={\frac {3}{8}}x-10} Slope = 38{\displaystyle {\frac {3}{8}}} , You can add, subtract, multiply, and more to isolate a variable, usually the "y." Just remember that, whatever you do to one side of the equal sign (like add 3) you must do to the other side as well.
Your final goal is an equation similar to y=mx+b{\displaystyle y=mx+b}.
For example:
Find the slope of 2y−3=8x+7{\displaystyle 2y-3=8x+7} Set to the form y=mx+b{\displaystyle y=mx+b}: 2y−3+3=8x+7+3{\displaystyle 2y-3+3=8x+7+3} 2y=8x+10{\displaystyle 2y=8x+10} 2y2=8x+102{\displaystyle {\frac {2y}{2}}={\frac {8x+10}{2}}} y=4x+5{\displaystyle y=4x+5} Find the slope:
Slope = M = 4
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