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User Tamikia
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a) The lines are parallel lines

b) The lines are perpendicular

c) The lines are intersecting lines.

How to determine parallelism, perpendicularity of lines.

a) y = -2x/3 + 7

-2x -3y = 12

-3y = 2x + 12

y = -2x/3 + 4

The slope of the two lines is -2/3.

Two lines are parallel when their slopes are equal.

Since the have equal slope , they are parallel lines that can never intersection.

b) Given

y - 6 = 1/4((x + 2) and y = -4x - 10

Let's write in the y = mx + b form to compare the lines.

y - 6 = x/4 + 1/2

The slope of the line is 1/4.

y = -4x - 10

The slope of the line is -4.

If m1m2 = -1

where

m1 is slope of equation 1

m2 is slope of equation 2

The lines are perpendicular

so,

1/4*(-4) = -1

Product of slopes is -1, the lines are perpendicular.

c) Given

2x - y = 7 and 3x - 4y = -8

-y = -2x + 7

y = 2x - 7

And

3x - 4y = -8

-4y = -3x -8

y = 3x/4 + 2

The lines have different slopes so, they are intersecting lines.

User Shaqwan
by
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