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Answer:
This is approximately the same as
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Explanation:
Solve the given equation for y
5x-y = 1
-y = -5x+1
y = 5x-1
slope of this line is m = 5 since it is in the form y = mx+b
Write m = 5 as m = 5/1
Flip the fraction: 5/1 ----> 1/5
Flip the sign: 1/5 ----> -1/5
The perpendicular slope is -1/5
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Let p and q be the x and y intercepts
So the equation we're after goes through the points (p,0) and (0,q)
The slope of the line through these points is
m = (y2-y1)/(x2-x1)
m = (q-0)/(0-p)
m = q/(-p)
m = -q/p
We want this slope to be -1/5 as this is the perpendicular slope we found earlier
-q/p = -1/5
q/p = 1/5
5q = 1p
p = 5q ... we will use this later
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The base of the triangle is p while the height is q
We want the area of the triangle to be 5 square units
area = 0.5*base*height
5 = 0.5*p*q
5 = 0.5*(5q)*q ... plug in p = 5q
5 = 2.5q^2
2.5q^2 = 5
q^2 = 5/2.5
q^2 = 2
q = sqrt(2)
p = 5*q
p = 5*sqrt(2)
The y intercept is b = q = sqrt(2), so
y = mx+b
See the diagram below.
