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Question 766576:
Answer by Shana-D77(132)   (Show Source):
You can put this solution on YOUR website! First, remember that parallel lines have the same slope and perpendicular lines have "opposite reciprocal" slopes. An example of perpendicular would be 4/3 vs. -3/4.
There are three forms of the linear equation, each useful for different things:
1)Slope-intercept form: useful to find slope and y-intercept
2) Standard Form: useful for finding x and y intercepts
3) Point-slope form: useful for finding the equation of the line with a given slope through a given point.
1) Your teacher gave these equations to you in Standard form (blah!). Let's convert to slope-intercept to find the slope:
-3x + 2y = -5
2y = 3x - 5 (added 3x to both sides)
y = 3/2x =- 5/2 (divided both sides by 2)
We now see the slope is 3/2. The perpendicular slope would be -2/3.
Next, "through (-2, -1)... Use point-slope form.
y - y1 = m(x - x1)
y - -1 = -2/3(x - -2)
y + 1 = -2/3(x + 2)
y + 1 = -2/3x - 4/3 (distributed the -2/3)
y = -2/3x - 7/3 (subtracted 1 from both sides)
Your other to questions can be answered in the exact same way EXCEPT that 2) is asking for parallel. In this case, use the same slope you get when converting -2x - 3y = -5 to slope-intercept form.
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