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.