Find a line that is parallel and perpendicular to y 3x 10

Find a line that is parallel and perpendicular to y = 3x + 10 through (-2. -2) a. Parallel b. Perpendicular Find a line that is parallel and perpendicular to y = 12x through (0, 12). a. Parallel b. Perpendicular Using the Pythagorean Theorem (a^2 + b^2 = c^2), find the following missing side lengths: Using the Pythagorean Theorem, figure out of the following triangles are right triangles.

Solution

Parallel lines have same slope

Perpendicular lines have negative slope and their slopes are reciprocal to each other.

Therefore given line is y=-3x + 1

Comparing it with standard equation y=mx+c

Where m is the slope and c is the y intercept.

We can say that the slope of the given line is m=-3

Therefore slope of line parallel to the given line will also be m=-3, since this line passes through (0,12) hence y intercept i.e c is 12 because y intercept is the point where x is 0.

Hence equation of line will be y=-3x+12

Similarly equation of line perpendicular to the given line will have slope m = -1/(-3) = 1/3 with y intercept c =12

Therefore equation of line perpendicular to given line is

y=(1/3)x + 12.

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