SOLUTION: Find the equation of the line perpedicular to x-4y=3 and passes through the point (2,10)

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Question 1198735: Find the equation of the line perpedicular to x-4y=3 and passes through the point (2,10)
Found 4 solutions by Theo, MathTherapy, josgarithmetic, greenestamps:
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
slope intercept of the straight line equation is y = mx + b
your equation is x - 4y = 3
add 4y to both sides of the equation and subtract 3 from both sides of the equation to get x - 3 = 4y
divide both sides of the equation by 4 to get x/4 - 3/4 = y
switch sides on the equation to get y = x/4 - 3/4
this is the same as y = 1/4 * x - 3/4
a line perpendicular to the line of this equation is has a slope that is a negative reciprocal of the line.
that would be a slope of -4
the line perpendicular to the given line is therefore y = -4 * x - 3/4
the more general form of that equation is y = -4 * x + b
to find the equation of that line that passes through the point (2,10), replace x with 2 and y with 10 to get 10 = -4 * 2 + b
simplify to get 10 = -8 + b
add 8 to both sides of that equation to get 18 = b
the equation of the line perpendicular to the given line and passing through the point (2,10) is y = -4 * x + 18
here's a graph of both lines.



the red line is the original line.
the blue line is the line perpendicular to it.
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

Find the equation of the line perpedicular to x-4y=3 and passes through the point (2,10)
Switch coefficients, then negate NEW "y" to get from: x - 4y to 4x + y. Right-side becomes: 4(2) + 10 = 18

Equation: 4x + y = 18. 

Answer by josgarithmetic(39618)   (Show Source): You can put this solution on YOUR website!
 







Slope must be  , for perpendicular line but not yet know constant on the right member.







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-

Equation wanted,;

If want in the same form as was given, then   

Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!
 


For an elementary solution, do what two of the other tutors do:

Put the given equation in slope-intercept form to find the slope;

Find the slope of the perpendicular line, which is the negative reciprocal of the slope of the given line; and

Use that slope and the given point with either the slope-intercept or standard form of a linear equation to find the equation.


Students with knowledge of only basic algebra should know that solution method.


For an easier solution, for students with a more extensive knowledge of math, do what tutor @MathTherapy does.


Given a linear equation in standard form Ax+By=C, the equation of a line perpendicular to the given line is of the form Bx-Ay=D (switch the coefficients and change the sign of one of them).


Then just plug in the coordinates of the given point to find the answer.


x-4y = 3 --> 4x+y = D

4(2)+10 = 18

ANSWER: 4x+y=18


 

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