Perpendicular Lines

Question

The equation y = 3/4X + 1 represents a given line.. Write the equation for the line that passes through (3,4) and is perpendicular to the given line

Answer 1

A line that passes perpendicular to a given line will have a slope that is opposite-reciprocal in value. Opposite means you flip the sign and reciprocal means you take the inverse. The given line y = (3/4)x + 1 has a slope of m = 3/4, so the slope of the perpendicular line will be m = -4/3. So far, the perpendicular line equation will look like this in slope-intercept form (y = mx + b):

y = (-4/3)x + b

The next step is to plug in the x and y coordinates of the given point (x, y) into the the y=mx + b equation of the perpendicular line. In this case the point is (3,4), so:

4 = (-4/3)(3) + b

The next step is to solve for b (the y-intercept):

b = 8

The last step is to insert the calculated value of b into the equation of the perpendicular line:

y = (-4/3)x + 8

Sometimes answers will show as rearranged equations, so you may see this:

y + (4/3)x = 8

Hope this helps and feel free to reach out!

Answer 2

The equation y = 3/4X + 1 represents a given line.. Write the equation for the line that passes through (3,4) and is perpendicular to the given line

Perpendicular lines have slopes that are the negative reciprocals of each other. That is, m and -1/m.

The slope of the given line is 3/4.

The slope of the perpendicular line is -4/3.

The formula for the perpendicular line looks like: y = -(4/3)x + b

We can use the point (3,4) to determine b.

4 = -(4/3)(3) + b

8 = b

The line y=-(4/3)x + 8 is perpendicular to the line y=(3/4)x + 1 and passes through the point (3,4).

Answer 3

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