We need to write an equation of a line in slope intercept form which is y= mx + b. So we need to know m (the slope) and b (the y intercept which is where the line crosses the y axis)
We know that the line we need the equation for is perpendicular to a given segment and also bisects the segment (meets it at the midpoint). The given segment runs between the two points (-3, 4) and (3, -8).
Step 1, find the midpoint of the given segment using the midpoint formula M = (
x_{1} + x_{2} , y_{1} + y_{2 )}
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It doesn't matter which point we call point one so lets label our points x_{1
}y_{1 }x_{2} y_{2}
(-3, 4) (3 ,-8)
Plugging these values into the formula we get M = ( -3 + 3 , 4 + -8 ) which results in a midpoint of (0, -2)
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So now we have a point for our line and in this example it happens to be the y intercept. You know this because the x value of the y intercept is always zero and the y value is b.
Step 2 we still need to find the slope of the given segment so we can use it to determine the slope of our line. Since the lines are perpendicular, we know the slope of our line will be the opposite inverse ( meaning flip the fraction over and change the sign) of the slope of the given segment.
slope m = y_{2} -y_{1} using the points x1 y1 x2 y2 we get
-8 - 4 = -12 = -2
x_{2} -x_{1 } (-3, 4) (3 ,-8) 3- -3 6
Since our line is perpendicular, our slope will be the opposite inverse of
-2 which is 1
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Now we just plug what we have found into the formula y =mx+b to get y=
1 X -2
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