SOLUTION: A line that is perpendicular to the line segment connected by (4,-2) and (6,-8) but passes through the point (12,-5) wh at is this is slope and General form

Question 980907: A line that is perpendicular to the line segment connected by (4,-2) and (6,-8) but passes through the point (12,-5) wh
at is this is slope and General form
Found 2 solutions by josgarithmetic, Cromlix:
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
Find the equation for either form, and convert (algebra steps) into the other form.

slope m, for the points (4,-2) and (6,-8):
.
The slope perpendicular to this is its negative reciprocal, which is .

The wanted equation using POINT-SLOPE FORM (because this is easier to arrange) is , and this line passes through (12,-5).

Convert the equation into slope intercept form, and into general form.

--
--
Slope-Intercept Form will look like y=mx+b
and
General Form will look like Ax+By=C.
Answer by Cromlix(4381) (Show Source): You can put this solution on YOUR website!
Hi there,
First work out gradient:
Gradient = y2 - y1/x2 - x1
Utilising (4,-2) and (6, -8)
-8 -(-2)/6 - 4
-8 + 2/6 - 4
-6/2
= -3
If two lines are perpendicular to one another
then their gradients multiply together to give -1
m1 x m2 = -1
So, -3 x m2 = - 1
m2 = 1/3
Next use line equation:
y - b = m(x - a)
Utilising m = 1/3 and (12, -5)
y -(-5) = 1/3(x - 12)
y + 5 = 1/3(x - 12)
y + 5 = 1/3x - 4
y = 1/3x -4 - 5
y = 1/3x - 9
or
3y = x - 27
Hope this helps:-)
RELATED QUESTIONS
Find the midpoint of the line segment with endpoints (-8,4) and (-2,-6) Find the... (answered by josgarithmetic)
write the equation of the line that passes through the point (2, -4) and is perpendicular (answered by rothauserc,greenestamps)
Write an equation of a line in slope intercept form that is perpendicular to the line 2x... (answered by ewatrrr)
Which choice is the equation of a line that passes through the point (�6, �2) and is... (answered by stanbon)
The equation of a line is given by y=(4/50)x-12 Find the equation of a line... (answered by richwmiller)
a) Find the intersection point for equations 5x + 3y = 12 and 10x � 2y = 8. b) Find... (answered by nant_87)
Write the equation of the line in point-slope form that passes through (5,-4) and is... (answered by josgarithmetic)
Find the equation of the line that passes through the point (-2, 4) and is perpendicular... (answered by josgarithmetic)
what is the equation of the line that passes through the point (-2,-5) and is... (answered by Alan3354)