I’m struggling can someone please help me

Question

What is the equation of the line that is perpendicular to 2x + 4y = 1 and that passes through the point (4,3)?

Answer 1

y = mx + b

2x + 4y = 1

2x - 2x + 4y = 1 - 2x

4y = -2x + 1

4y/4 = (-2x + 1)/4

y = (-1/2)x + 1/4

Perpendicular lines have opposite, reciprocal slopes.

y = mx + b

3 = 2(4) + b

3 = 8 + b

b = -5

y = 2x - 5

Answer 2

To find the slope of the perpendicular you need to first find the slope of 2x+4y=1. You do that by transforming that equation into slope intercept form by solving for y.

4y = -2x +1

y = -2x/4 + 1/4 = -1x/2 + 1/4

So the slope of the given line is -1/2.

Since perpendicular lines have slopes that are negative reciprocals the slope of the perpendicular must be:

m_{perpendicular}= - (-2/1) = 2.

Now use the point-slope formula for the equation of a line (since you know the slope and a point):

y - 3 = 2 (x-4)

y -3 = 2x-8

y = 2x-5

Note you also could have found the equation by starting with slope intercept (substituting 4 for x, 3 for y, and 2 for m in order to solve for b). Which one you use is just a personal preference.

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