SOLUTION: 1.Use the given conditions to write an equation for the line in the indicated form. Passing through (3, 4) and perpendicular to the line whose equation is -2x+y-2=0 slope-inter

Algebra ->  Customizable Word Problem Solvers  -> Finance -> SOLUTION: 1.Use the given conditions to write an equation for the line in the indicated form. Passing through (3, 4) and perpendicular to the line whose equation is -2x+y-2=0 slope-inter      Log On

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Question 1119703: 1.Use the given conditions to write an equation for the line in the indicated form.
Passing through (3, 4) and perpendicular to the line whose equation is -2x+y-2=0
slope-intercept form?
2.Find and simplify the difference quotient {-f(x)+f(h+x)}/h, h different 0 for the given function.
f(x) = x2 + 4x - 5





Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
The equation of the line may be rewritten as y=2x+2 and has slope 2
The line perpendicular to it has slope -1/2, the negative reciprocal.
y-y1=m(x-x1) point slope formula where m is slope and (x1, y1) point
y-4=(-1/2)(x-3)
y=-x/2 + 11/2
graph%28300%2C300%2C-10%2C10%2C-10%2C10%2C2x%2B2%2C%28-x%2F2%29%2B%2811%2F2%29%29
This is (x^2+2xh+h^2+4x+4h-5-(x^2+4x-5) divided by h
The numerator becomes 2xh+h^2+4h, the denominator h
This simplifies to 2x+h+4 and as h goes to 0, that becomes 2x+4, which is the derivative
f(x+h) for the function is (x+h)^2+4(x+h)-5, which is where the numerator came from.