Question 644646: The question states: Find an equation for the line.
4. through (-8,8) and parallel to y = 3/2x -3. I have a test on tuesday and cant figure out the steps to work this problem out. Can you please help me.
5. through (-3,8) and vertical
6. through (-7,5) and perpendicular to y=2/3x -2
Can someone walk me through the steps in solving these questions. Thanks
Found 2 solutions by nerdybill, MathLover1:
Answer by nerdybill(7384)   (Show Source):
You can put this solution on YOUR website! you have to know a few things:
two forms of an equation of a line:
y = mx + b (slope-intercept form)
where
m is slope
b is y-intercept at (0,b)
.
y-y1 = m(x - x1) (point-slope form: used to derive equation of a line give one point and the slope)
.
if two lines are "parallel" their slopes are equal
.
if two lines are "perpendicular" their slopes are "negative reciprocal" (equals -1 when multiplied together)
.
.
4. through (-8,8) and parallel to y = 3/2x -3.
slope of new line is 3/2
crossing (-8,8)
plug into "point-slope" form:
y-y1 = m(x - x1)
y-8 = (3/2)(x - (-8))
y-8 = (3/2)(x + 8)
y-8 = (3/2)x + (3/2)8
y-8 = (3/2)x + 12
y = (3/2)x + 20 (answer in "slope-intercept" form)
.
5. through (-3,8) and vertical
x = -3
.
6. through (-7,5) and perpendicular to y=2/3x -2
since slope of:
y=2/3x -2
is 2/3.
Our new slope is -3/2 (because -3/2 * 2/3 = -1)
crossing (-7,5)
plug into "point-slope" form:
y-y1 = m(x - x1)
y-5 = (-3/2)(x - (-7))
y-5 = (-3/2)(x + 7)
y-5 = (-3/2)x + (-3/2)7
y-5 = (-3/2)x - 21/2
y = (-3/2)x - 21/2 + 5
y = (-3/2)x - 21/2 + 10/2
y = (-3/2)x - 11/2 (answer in "slope-intercept" form)
Answer by MathLover1(20850)  (Show Source):
You can put this solution on YOUR website! 4. through ( , ) and  to  .
| Solved by pluggable solver: Finding the Equation of a Line Parallel or Perpendicular to a Given Line |
Since any two parallel lines have the same slope we know the slope of the unknown line is  (its from the slope of  which is also ).
Also since the unknown line goes through (-8,8), we can find the equation by plugging in this info into the point-slope formula
Point-Slope Formula:
 where m is the slope and ( , ) is the given point
 Plug in  ,  , and 
 Distribute
 Multiply
 Add to both sides to isolate y
 Combine like terms
So the equation of the line that is parallel to and goes through (,) is
So here are the graphs of the equations and
 graph of the given equation (red) and graph of the line (green) that is parallel to the given graph and goes through (,)
|
5. through ( ,) and  ... I guess to line
| Solved by pluggable solver: Finding the Equation of a Line Parallel or Perpendicular to a Given Line |
Remember, any two perpendicular lines are negative reciprocals of each other. So if you're given the slope of , you can find the perpendicular slope by this formula:
 where  is the perpendicular slope
 So plug in the given slope to find the perpendicular slope
 When you divide fractions, you multiply the first fraction (which is really  ) by the reciprocal of the second
 Multiply the fractions.
So the perpendicular slope is 
So now we know the slope of the unknown line is (its the negative reciprocal of from the line ).
Also since the unknown line goes through (-3,8), we can find the equation by plugging in this info into the point-slope formula
Point-Slope Formula:
where m is the slope and (,) is the given point
 Plug in  ,  , and
 Distribute
 Multiply
 Add to both sides to isolate y
 Combine like terms
So the equation of the line that is perpendicular to and goes through (,) is
So here are the graphs of the equations and
 graph of the given equation (red) and graph of the line (green) that is perpendicular to the given graph and goes through (,)
|
6. through ( , ) and perpendicular to 
| Solved by pluggable solver: Finding the Equation of a Line Parallel or Perpendicular to a Given Line |
Remember, any two perpendicular lines are negative reciprocals of each other. So if you're given the slope of  , you can find the perpendicular slope by this formula:
where is the perpendicular slope
 So plug in the given slope to find the perpendicular slope
 When you divide fractions, you multiply the first fraction (which is really ) by the reciprocal of the second
|
I think you can't see everything here and I will write remaining part:
So the perpendicular slope is 
So now we know the slope of the unknown line is (its the negative reciprocal of  from the line  . Also since the unknown line goes through (,), we can find the equation by plugging in this info into the point-slope formula
Point-Slope Formula:
 where m is the slope and ( , ) is the given point
So the equation of the line that is perpendicular to and goes through (,) is
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