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Question 324900: Line 1 crosses the y-axis at y=5 and passes through the point (2,1). Line 2 is perpendicular to Line 1 and crosses the x axis at x=-3. What is the equation for line 2?
Answer by nerdybill(7384)   (Show Source):
You can put this solution on YOUR website! Line 1 crosses the y-axis at y=5 and passes through the point (2,1). Line 2 is perpendicular to Line 1 and crosses the x axis at x=-3. What is the equation for line 2?
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First, determine slope of line 1:
From: "crosses the y-axis at y=5" we get one point (0,5)
And, using the other given point (2,1) we can calculate the slope:
(y2-y1)/(x2-x1) = (5-1)/(2-0) = 4/2 = 2
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Since line 2 is perpendicular (the slopes are negative reciprocals):
Let m = slope of line 2
then
2m = -1
m = -1/2 (Line 2 slope)
That, along with "crosses the x axis at x=-3" gives us a point at (-3, 0)
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Plug the above into the "point-slope" formula:
y - y1 = m(x - x1)
y - 0 = (-1/2)(x - (-3))
y = (-1/2)(x + 3)
y = (-1/2)x - 3/2 (this is what they're looking for)
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