SOLUTION: Two lines are perpendicular if Line 1 through (-4, 1) and (-2, -3) and Line 2 through (2, 1)

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Question 1003267: Two lines are perpendicular if Line 1 through (-4, 1) and (-2, -3) and Line 2 through (2, 1)

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

given:
Two lines are perpendicular: means their slopes are negative reciprocals to each other
if the slope of line 1 is m, then the slope of line 2 is m%5Bp%5D=-1%2Fm

Line 1 through (-4,+1) and (-2,+-3):
find the slope-intercept form of the equation or y+=+mx+%2B+b for this line using given points
Solved by pluggable solver: Find the equation of line going through points
hahaWe are trying to find equation of form y=ax+b, where a is slope, and b is intercept, which passes through points (x1, y1) = (-4, 1) and (x2, y2) = (-2, -3).
Slope a is a+=+%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29+=+%28-3-1%29%2F%28-2--4%29+=+-2.
Intercept is found from equation a%2Ax%5B1%5D%2Bb+=+y%5B1%5D, or -2%2A-4+%2Bb+=+-7. From that,
intercept b is b=y%5B1%5D-a%2Ax%5B1%5D, or b=1--2%2A-4+=+-7.

y=(-2)x + (-7)

Your graph:




so, your line 1 has equation y=-2x-7, and its slope is m=-2
now find negative reciprocal m%5Bp%5D=-1%2Fm
m%5Bp%5D=-1%2F-2
m%5Bp%5D=1%2F2
so far the equation of line 2 is y=%281%2F2%29x%2Bb
since given that Line 2 through (2,+1) =(x,+y), use this point to find b
1=%281%2F2%292%2Bb
1=1%2Bb
b=1-1
b=0
now we have the equation of line 2: y=%281%2F2%29x%2B0 or y=%281%2F2%29x

see them on a graph: