SOLUTION: Please show all work including all steps so that I may understand, thank you!! Consider the point P = (2, 8) and the line L, given by the equation 6x - 3y = 15. A. Write an e

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Question 938111: Please show all work including all steps so that I may understand, thank you!!
Consider the point P = (2, 8) and the line L, given by the equation 6x - 3y = 15.
A. Write an equation in slope-intercept of the line passing through P and parallel to line L.
B. Write an equation in slope-intercept of the line passing through P and perpendicular to line L.
Found 2 solutions by MathLover1, ewatrrr:
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!

the point = (, ) and
the line , given by the equation
in slope-intercept form
A. Write an equation in slope-intercept of the line passing through and to line .

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 (2,8), 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 (,)





B. Write an equation in slope-intercept of the line passing through P and 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 (2,8), 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

Make into equivalent fractions with equal denominators



Combine the fractions



Reduce any fractions

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 (,)
Answer by ewatrrr(24785)   (Show Source): You can put this solution on YOUR website!
the standard slope-intercept form for an equation of a line is

where m is the slope and b the y-intercept
...
the line L, given by the equation 6x - 3y = 15 0r y = 2x - 5(Green), m = 2
***Using point-slope form, P(2,8)
A. parallel to L, m = 2/1
y - 8 = 2(x-2)
y = 2x + 4 (Blue) 0r 2x-y = -4
....
B. perpendicular to L, m = -1/2 (negative reciprocal of 2
y - 8 = -1/2(x-2)
y = (-1/2)x + 9(Purple) 0r x + 2y = 18
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