First lets find the slope through the points (,) and (,)
Start with the slope formula (note: (,) is the first point (,) and (,) is the second point (,))
Plug in ,,, (these are the coordinates of given points)
Subtract the terms in the numerator to get . Subtract the terms in the denominator to get
Reduce
So the slope is
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Now let's use the point-slope formula to find the equation of the line:
------Point-Slope Formula------
where is the slope, and (,) is one of the given points
So lets use the Point-Slope Formula to find the equation of the line
Plug in , , and (these values are given)
Rewrite as
Distribute
Multiply and to get . Now reduce to get
Add to both sides to isolate y
Combine like terms and to get
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Answer:
So the equation of the line which goes through the points (,) and (,) is:
The equation is now in form (which is slope-intercept form) where the slope is and the y-intercept is
Notice if we graph the equation and plot the points (,) and (,), we get this: (note: if you need help with graphing, check out this solver)
Graph of through the points (,) and (,)
Notice how the two points lie on the line. This graphically verifies our answer.
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