Expert: Richard J. Raridon - 1/12/2010

Question
Im 24, Im in college. i have a few problems i can't figure out.
Find the slope and y-intercept for each line that has a slope
and y-intercept.
*x - y = 4

Write each equation in standard form using only integers
*y = - 2/3 x-  5/6


Graph each line using its y-intercept and slope
*2x + y = 0

In each case determine whether the lines are parallel,
perpendicular, or neither.
*y = 3x + 2
y = 1/3 x-4

*y = 1/3 x+ 1/2
y = 1/3 x-2


Answer
one standard equation is y = mx+b, where m is the slope and b is the y-intercept.  
So you write the equation in that form
x-y = 4, y = x-4 so the slope is 1 and the y-intercept is -4
y = (-2/3)x -5/6.  Write it that way since -2/3x could be interpreted as having 3x in the denominator.  Then multiply each term by 6 to get 6y = -3x -5 or 3x+6y-5 = 0
2x+y = 0 or y = -2x.  the slope is -2 and the y-intercept is 0.  It only takes two points to plot a straight line.  So if x=0, y=0 and if x = 1, y = -2.  
y = 3x+2 and y = (1/3)x-4.  the lines are not parallel since the slopes are different.  to be perpendicular, one slope is the negative reciprocal of the other.  not true in this case so the answer is neither.
y = (1/3)x+1/2 and y = (1/3)x-2, lines are parallel.