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Question 174054: WRITE AN EQUATION OF A LINE THAT PASSES THROUGH THE GIVEN POINT IS PERPENDICULAR TO THE GIVEN LINE.
PROBLEM: (1,-1), Y=3X+2
PLEASE ANSWER AND GIVE ME THE STEPS TO SOLVE PROBLEMS SIMILAR TO THE ONE ABOVE.
PLEASE EXPLAIN SO THAT I CAN MEMORIZE THE STEPS
Found 3 solutions by stanbon, Earlsdon, monika_p:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Write an equation of the line that passes through the given point and is perpendicular to the given line.
(1,-1), y=3x+2
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Since the given slope is 3, the slope you want is -1/3.
Equation form is y = mx +b
Substitute to solve for "b":
-1 = (-1/3)*1 + b
b = -1 + (1/3) = -2/3
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Equation:
y = (-1/3)x + (-2/3)
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Cheers,
Stan H.
Answer by Earlsdon(6294) (Show Source):
You can put this solution on YOUR website! First, recall that if two lines are perpendicular to each other, then their slopes are the negative reciprocal of each other. In other words, if you were to multiply the slopes of two perpendicular lines, the result would be -1.
So first you need to find the slope of the line represented by the given equation: y = 3x+2.
Since this equation is already in the "slope-intercept" form: y = mx+b, you can see that its slope, m = 3, so the negative reciprocal of 3 is  and this will be the slope of the new line. You can then start the equation of the new line with:
 Next, you need to find the value of b, the y-intercept. You can do this by substituting the x- and y-coordinates of the given point (1, -1) into the equation above:
 Now you can solve this for the value of b. Add  to both sides.
 Simplify the left side.
 Now you can write the final equation for the new line.
Answer by monika_p(71) (Show Source):
You can put this solution on YOUR website! Basic equation of the line : y=mx+b, where m is a slope
If two lines are perpendicular it means that if one has slope m1 then the other one has m2=-1/m1 (negative reciprocal)
Equation of the line passing through point (x1,y1):
y – y1 = m(x – x1)
1. find the slope of line 2
if line1 y=3x+2 has slope m1=3, then slope of line2
m2=-1/m1=-1/3
2.substitute m2,(x1, y1)=(1,-1)
y-y1=m(x-x1)
y-(-1)=-1/3(x-1)
y+1=-1/3x+1/3
3.write equation in basic form
y=-1/3x-2/3---answer
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