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Question 428573: What is the equation of the line, in standard form, that passes through (4, -3) and is parallel to the line whose equation is 4x + y - 2 = 0?
Found 3 solutions by mananth, ikleyn, MathTherapy:
Answer by mananth(16949)   (Show Source):
You can put this solution on YOUR website! 4x+y=2
Find the slope of this line
y=-4x+2
y=-4x+2
Compare this equation with y=mx+b
slope m = -4
The slope of a line parallel to the above line will be the same
The slope of the required line will be -4
m=-4,point(4,-3)
Find b by plugging the values of m & the point in
y=mx+b
-3=-16.00+b
b=13
m=-4
Plug value of the slope and b
The required equation is y=-4x+13
Answer by ikleyn(53419)  (Show Source):
You can put this solution on YOUR website! .
What is the equation of the line, in standard form, that passes through (4, -3) and is parallel to the line
whose equation is 4x + y - 2 = 0?
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It can be solved in much more efficient way than @mananth does it in his post.
The given line equation is 4x + y - 2 = 0.
It is the same as
4x + y = 2. (1)
Any parallel line has the form
4x + y = c (2)
with the same form '4x + y' in the left side and some constant 'c' in the right side.
To find 'c', we substitute coordinates of the given point (4,-3) into equation (2).
We get
4*4 + (-3) = 16 - 3 = 13 = c.
Thus the sough equation is
4x + y = 13.
It is the "standard form" line equation.
ANSWER. The "standard form" line equation is 4x + y = 13.
Solved.
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Two post-solution notices
(1) Doing this way, you should not worry about the slope.
(2) The final equation in the @mananth post is NOT a standard form.
Answer by MathTherapy(10585)  (Show Source):
You can put this solution on YOUR website!
What is the equation of the line, in standard form, that passes through (4, -3) and is parallel to the line whose equation is 4x + y - 2 = 0?
Equation that sought-equation is parallel to: 4x + y - 2 = 0, or in STANDARD form: 4x + y = 2
As the lines are parallel, left-side of sought-equation is the same.
We then get: 4x + y = 4(x) + y
4x + y = 4(4) + - 3 ----- Substituting given point, (4, - 3), on right-side
4x + y = 16 - 3
4x + y = 13 <=== Sought-equation, in STANDARD FORM
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