Answer:
Line 1 and 2: perpendicular
Line 1 and 3: parallel
Line 2 and 3: perpendicular
Step-by-step explanation:
Given:
line 1: y = -3/5x - 3
line 2: 10x - 6y = 6
line 3: 5y = - 3x + 6
To find:
To determine if each pair of lines is parallel, perpendicular or neither
To determine the above, we need to know the slope of each of the line
line 1 is already in the form y = mx + b
m = slope
As a result, slope of line 1 = -3/5
line 2:
10x - 6y = 6
-6y = -10x + 6
y = -10x/-6 + (6/-6)
y = 5/3x - 1
slope of line 2 = 5/3
line 3:
5y = -3x + 6
y = -3x/5 + 6/5
slope of line 3 = -3/5
Line 1 and 2:
The slopes are not equal. we check if they would be per perpendicular
For two lines to be perpendicular, the slope of 1 will be the negative reciprocal of the other.
slope of line 1 = -3/5
reciprocal of the line = -5/3
negative reciprocal = -(-5/3) = 5/3
5/3 is the slope of line 2
The slope of 2 is the negative reciprocal of the slope of line 1
The lines are perpendicular
Line 1 and 3: Both have the same slopes
For two lines to have the same slopes, they will be parallel
Line 2 and 3:
slope of line 2 = 5/3
slope of line 3 = -3/5
reciprocal of the line 2= 3/5
negative reciprocal = -3/5
Slope of line 2 is the negative reciprocal of the slope of line 3
line 2 and line 3 are perpendicular