Question

Choose the equation of the line through (4, –5) and perpendicular to 6x + 12y = 13.

A. y=-1/2x-3
B. y=1/2x-7
C. y=2x-13
D. None of these

Answer 1

The equation of the line through (4, -5) and perpendicular to 6x + 12y = 13 is y = 2x - 3.

Step-by-step explanation:

To find the equation of a line perpendicular to another line, we need to determine the slope of the given line and then find the negative reciprocal of that slope. The given line is 6x + 12y = 13, which can be rewritten as y = (-1/2)x + (13/12). The slope of this line is -1/2, so the slope of the line perpendicular to it is 2. Using the point-slope form of a linear equation, we can substitute the values x = 4, y = -5, and m = 2 into the equation y - y1 = m(x - x1) to get the equation of the desired line: y - (-5) = 2(x - 4) which simplifies to y = 2x - 3. Therefore, the equation of the line through (4, -5) and perpendicular to 6x + 12y = 13 is y = 2x - 3.

Answer 2

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Step-by-step explanation: