1. Determine if two lines are parallel 5x+2y-11=0 and 15x+6y-11=0Solution:When two lines are parallel, their slopes are equal.
1. Slope of line
5x+2y-11=05x+2y-11=0:. 2y=-5x+11:. y=-(5x)/(2)+11/2:. Slope
m_1=-5/22. Slope of line
15x+6y-11=015x+6y-11=0:. 6y=-15x+11:. y=-(5x)/(2)+11/6:. Slope
m_2=-5/2Here
m_1=m_2, so these two lines are parallel
2. Determine if two lines are parallel x-2y+15=0 and 2x-4y-4=0Solution:When two lines are parallel, their slopes are equal.
1. Slope of line
x-2y+15=0x-2y+15=0:. 2y=x+15:. y=(x)/(2)+15/2:. Slope
m_1=1/22. Slope of line
2x-4y-4=02x-4y-4=0:. 4y=2x-4:. y=(x)/(2)-1:. Slope
m_2=1/2Here
m_1=m_2, so these two lines are parallel
3. Determine if two lines are parallel x-y=1 and 2x-3y+1=0Solution:When two lines are parallel, their slopes are equal.
1. Slope of line
x-y=1x-y=1:. y=x-1:. Slope
m_1=12. Slope of line
2x-3y+1=02x-3y+1=0:. 3y=2x+1:. y=(2x)/(3)+1/3:. Slope
m_2=2/3Here
m_1!=m_2, so these two lines are not parallel
4. Determine if two lines are parallel x-2y+15=0 and 3x+y-4=0Solution:When two lines are parallel, their slopes are equal.
1. Slope of line
x-2y+15=0x-2y+15=0:. 2y=x+15:. y=(x)/(2)+15/2:. Slope
m_1=1/22. Slope of line
3x+y-4=03x+y-4=0:. y=-3x+4:. Slope
m_2=-3Here
m_1!=m_2, so these two lines are not parallel
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