Find an equation of the line that passes through the point (3,8) and is (a.) parallel to and (b) perpendicular to the line -4x+7y=-5.
2006-09-12 15:34:32 · 6 answers · asked by *shy*earthangel* 1 in Science & Mathematics ➔ Mathematics
the slope of -4x+7y=-5 is 7/4
parallel to have the same slope
y - 8 = 7/4(x-3)
4(y-8) = 7x - 21
4y -32 = 7x -21
4y-7x = 11
perpendicular has the negative reciprocal slope which is -4/7
y - 8 = -4/7(x-3)
7y - 56 = -4x +12
7y + 4x = 68
goodluck ^_^
2006-09-12 15:45:43 · answer #1 · answered by ettezzil 5 · 0⤊ 0⤋
a) Parallel lines have the same slopes.
Slope of line -4x + 7y = -5
Solve for y
7y = 4x - 5
y = (4/7)x - (5/7); (4/7) is the slope [y = mx + b...]
Therefore the slope of the parallel line is also (4/7)
Use the point slope formula for the equation with (3,8):
y - y1 = m(x - x1)
y - 8 = (4/7)(x - 3)
y = (4/7)x - (12/7) + 8
y = (4/7)x - (12/7) + (56/7)
y = (4/7)x + (44/7)
7y = 4x + 44
-4x + 7y = 44
b) Perpendicular lines have the negative reciprocal slopes.
(4/7) is the slope so.... (-7/4) is the negative reciprocal
Use the point slope formula again with (3,8):
y - y1 = m(x - x1)
y - 8 = (-7/4)(x - 3)
y = (-7/4)x + (21/4) + 8
y = (-7/4)x + (21/4) + (32/4)
y = (-7/4)x + (53/4)
4y = -7x + 53
7x + 4y = 53
2006-09-12 22:43:34 · answer #2 · answered by Anonymous · 0⤊ 0⤋
I believe problem not stated properly. I believe asking for 2 separate answers. A line can not be parallel and perpendicular to another line. -4x+7y=b put in (3,8) find b. that's the parallel one.
Now change to 4x-7y=q put in (3,8) find q. That is the perpendicular one thru the point.
good luck
2006-09-12 22:59:01 · answer #3 · answered by rwbblb46 4 · 0⤊ 0⤋
at least try to do your own homework instead of just asking for answer.
1. find the slope of the line (hint: parallel to -4+7y=5)
2. use the coordinate (3,8) to determine the position of the line
2006-09-12 22:42:39 · answer #4 · answered by Anonymous · 0⤊ 1⤋
-4x+7y=-5
==>7y=4x-5
==>y=(4/7)x-(5/7)
slope is 4/7
a). parallel, same slope
(y-8)=(4/7)(x-3)
==>7(y-8)=4(x-3)
or 7y-4x=44
b). perpendicular, slope is inverse of the original or -1/(4/7) or -7/4
(y-8)=(-7/4)(x-3)
=>4(y-8)=-7(x-3)
or 4y+7x=53
2006-09-12 22:49:47 · answer #5 · answered by mike-yhqna 1 · 0⤊ 0⤋
-4x + 7y = -5
7y = 4x - 5
y = (4/7)x - (5/7)
a.)
(3,8), m = (4/7)
8 = (4/7)(3) + b
8 = (12/7) + b
56 = 12 + 7b
7b = 44
b = (44/7)
ANS : y = (4/7)x + (44/7)
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b.)
(3,8), m = (-7/4)
8 = (-7/4)(3) + b
8 = (-21/4) + b
32 = -21 + 4b
4b = 53
b = (53/4)
ANS : y = (-7/4)x + (53/4)
2006-09-12 22:49:53 · answer #6 · answered by Sherman81 6 · 0⤊ 0⤋