Answer:
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
