What is the equation for the line through P that is parallel to L and perpendicular to L. P(0,0), L:y=-x+2

A. The equation of the line parallel to line L is y = – x

B. The equation of the line perpendicular to line L is y = x

Step-by-step explanation:

We'll begin by calculating the slope of line L.

This can be obtained as follow:

y = –x + 2

Comparing the above equation with:

y = mx + c

We can see that the slope (m) = –1.

Therefore, the slope of line L is –1

A. Determination of the equation of the line parallel to line L. This is illustrated below:

When two lines are parallel, their slope (m) is equal i.e

m1 = m2

m1 = – 1

– 1 = m2

This means that the slope of the line parallel to line L is –1

Now we shall determine the equation of the line parallel to line L as follow:

Coordinate = (0, 0)

x1 coordinate = 0

y1 coordinate = 0

Slope (m) = –1

y – y1 = m(x – x1)

y – 0 = –1 (x – 0)

y = – x

Therefore, the equation of the line parallel to line L is y = – x

B. Determination of the equation of the line perpendicular to line L. This is illustrated below:

When two lines are perpendicular, the product of their slope (m) is –1 i.e

m1 • m2 = – 1

but m1 = –1

–1 x m2 = – 1

Divide both side by – 1

m2 = –1/–1

m2 = 1

Now, we shall determine the equation of the line perpendicular to line L as follow:

Coordinate = (0, 0)

x1 coordinate = 0

y1 coordinate = 0

Slope (m) = 1

y – y1 = m(x – x1)

y – 0 = 1 (x – 0)

y = x

Therefore, the equation of the line perpendicular to line L is y = x

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