Question 122982: Hi, my son just started a new school on Tues. Has an Algebra worksheet that he doesn't understand. I am normally able to help him, but I do not know how to do this type of problem.
1. Determine if the graphs of the equations y=2/3 and 3x+2=6 are parallel, perpendicular or neither.
2. Write an equation for the line that is paralled to y=1/2x-1. Tell how you know they are parallel.
3. Find the slope of the lines perpendicular to the graph of 3x-y=11.
4. Write an equation of the line that passes through (5,3) and is parallel to x+3y=6.
Any help or explanations would be greatly appreciated.
Answer by scott8148(6628)   (Show Source):
You can put this solution on YOUR website! if you get the equations into slope-intercept form (y by itself on one side of the equation)
__ the coefficient of the x term equals the slope of the line, and the constant term is the y-intercept
__ (the value of y where the line crosses the y-axis)
the general form is y=mx+b __ m is the slope, b is the y-intercept
if the slopes of the lines are the same, the lines are parallel
if the slopes are negative reciprocals (product of the slopes is -1), the lines are perpendicular
1. y=2/3 has no x term, so it is a horizontal line (m=0, b=2/3)
__ 3x+2=6 has no y term, so it is a vertical line (m is undefined and b does not exist)
__ a horizontal line and a vertical line are perpendicular to each other
2. y=1/2x+b (for any value of b)
__ you know they are parallel because they have the same slope (m=1/2)
3. 3x-y=11 __ 3x-11=y, so the slope is 3 __ any line with a slope of -1/3 is perpendicular __ y=-1/3x+b
4. parallel means same slope __ 3y=-x+6 __ y=-1/3x+2 __ use (5,3) to find new value for b
__ 3=(-1/3)5+b __ 3=-5/3+b __ 14/3=b __ y=-1/3x+14/3 or 3y=-x+14
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