SOLUTION: Suppose the line through points (-1,6) and (x,2) is perpendicular to the graph of 2x + y = 3. Find the value of x
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-> SOLUTION: Suppose the line through points (-1,6) and (x,2) is perpendicular to the graph of 2x + y = 3. Find the value of x
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Question 410222: Suppose the line through points (-1,6) and (x,2) is perpendicular to the graph of 2x + y = 3. Find the value of x Found 2 solutions by nerdybill, solver91311:Answer by nerdybill(7384) (Show Source):
You can put this solution on YOUR website! Suppose the line through points (-1,6) and (x,2) is perpendicular to the graph of 2x + y = 3. Find the value of x
.
Find slope of
2x + y = 3
by rearranging into the "slope-intercept" form:
2x + y = 3
y = -2x + 3
slope then, is -2
.
A line perpendicular to this must have a slope that is the "negative reciprocal":
-2m = -1
m = 1/2
.
slope of (-1,6) and (x,2)
(y2-y1)/(x2-x1) = 1/2
(2-(-6))/(x-(-1)) = 1/2
(2+6)/(x+1) = 1/2
8/(x+1) = 1/2
cross-multiply:
16 = x+1
15 = x
Step 1: Determine the slope of the line represented by the given equation.
Step 2: Determine the slope of any line perpendicular to the line represented by the given equation using the fact that perpendiculars have slopes that are negative reciprocals:
Step 3: Use the slope formula to determine an expression in for the slope of the line that passes through the two given points.
where and are the coordinates of the given points.
Step 4: Set the expression derived in Step 3 equal to the slope value determined in Step 2. Solve for .
John
My calculator said it, I believe it, that settles it
