Question 174362: Find an equation of the line that is parallel to the line y=-4/3x+7 and that passes through the point (7,3).
Found 4 solutions by nerdybill, Mathtut, Alan3354, Electrified_Levi:
Answer by nerdybill(7384)   (Show Source):
You can put this solution on YOUR website! Find an equation of the line that is parallel to the line
If a line is to be parallel to:
y=-4/3x+7
It must have the same slope: -4/3
That, along with the given point of (7,3) is plugged into the "point-slope" form:
y-y1 = m(x-x1)
y-3 = (-4/3)(x-7)
y-3 = (-4/3)(x)- 7(-4/3)
y-3 = (-4/3)(x)+ 28/3
y = (-4/3)(x)+ 28/3 +3
y = (-4/3)(x)+ 28/3 + 9/3
y = (-4/3)(x)+ 37/3 (this is what you're looking for)
Answer by Mathtut(3670)  (Show Source):
You can put this solution on YOUR website! lines that are parallel have equal slopes so the slope of the line we are looking for has a slope of -4/3
:
using the point slope formula
:
y-3=-4/3(x-7)
:
y-3=-4/3(x)+28/3......multiply terms by 3
:
3y-9=-4x+28
:
Answer by Alan3354(69443)  (Show Source):
You can put this solution on YOUR website! Find an equation of the line that is parallel to the line y=-4/3x+7 and that passes through the point (7,3).
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It's not "an equation", it's the equation. There's only one.
y=-4/3x+7
The slope is -4/3, as the eqn is in the slope-intercept form.
Any line parallel to it will have the same slope.
So,
y-y1 = m*(x-x1) (m is the slope)
y-3 = (-4/3)*(x-7)
3y-9 = -4*(x-7)
3y-0 = -4x+28
4x+3y = 28
Answer by Electrified_Levi(103) (Show Source):
You can put this solution on YOUR website! Hi, Hope I can help,
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Find an equation of the line that is parallel to the line  and that passes through the point (7,3)
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We are trying to find a line parallel to this line
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lines are given in the form  , where "m" is the slope, and "b" is the y intercept
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, this line has a slope of  , and y intercept of "7"
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We are trying to find a parallel line, so that means the line will have the same slope as the other, or
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If we took the line form , we can start replacing the letters for our unknown line
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We know that "m" is , since it is parallel to the given line
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Our new formula is
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 ( we replaced "m" with the known slope )
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, we now have 3 variables, we will have to get rid of 2 of them
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We are also given a point, (7,3)
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Points are in the form of (x,y)
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(7,3):(x,y)
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x = 7
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y = 3
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, now replace the "x" and "y" with the numbers
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=  = 
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Now we just need to solve for "b"
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, we will move the  over to the left side
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=  =  = =  , or 
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You can check your answer by replacing "b" with  in the equation
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=  =  =  (True)
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Now just replace "b" in our original equation ( one where we had "x" and "y" )
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= 
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is the line in point slope form, if you want it in standard form  , here is how you would convert it
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, you would first multiply each side by "3"
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=  , using distribution
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 =  = 
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= 
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Now we need to move (-4x) to the left side
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=  = 
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Rearranging the left side
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=  , this is the standard form of the equation
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If you want to see if a point is on a line you would replace "x" and "y" with the point (x,y)
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Our point is (7,3)(x,y)
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x = 7
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y = 3
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=  =  =  (True)
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The graph of this line is
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It is parallel to the original line and has (7,3) as a point
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Your line that you were looking for or your answer is
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Standard form:
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Point-Slope form:
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Hope I helped, Levi
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