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Question 868430: Find the equation of the line through (0,1) and perpendicular to the line 3x+4y=5.
choices: A. 4x-3y=5, B. 4x-3y=-3, C. 5x-3y=4, D. 3x+4y=-4
Answer by JLJL(8)   (Show Source):
You can put this solution on YOUR website! From the question, we know there are 2 different straight lines intersecting to each other in perpendicular manner.
From the given equation of the first straight line, 3x + 4y = 5, we can find its gradient by rearranging the equation in the form of Y = mX + C, the step is shown as below.
3x + 4y = 5
4y = -3x + 5
y = -(3/4)x + (5/4)
When comparing with Y = mX + C, where m is the gradient. We can know the value of the gradient of the first straight line, m1 = -(3/4)
When two lines are perpendicular to each other, the product of gradient of the two lines must be equal to -1.
We can now calculate the value of the gradient of the second straight line as below.
m1 x m2 = -1
(-3/4) x m2 = -1
m2 = [(-1)x4]/[-3]
m2 = 4/3
To find the equation of the second straight line at point (0, 1), use the formula, y2 - y1 = m(x2 - x1)
y2 - 1 = (4/3)(x2 - 0)
y2 = (4/3)x2 + 1
3y2 = 4x2 + 3
Rearranging 3y = 4x + 3, we can get 4x - 3y = -3. Therefore, The answer is B.
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