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Question 84892: For the linear equation in standard form 2x+5y=6:
a) Find the slope of this line
b) Find the slope of a line parallel to this line
c) Find the slope of a line perpendicular to this line
d) use your answers to part c) to write the equation of the line which is perpendicular to the given line and passes through the point (-3,-4). Put final equation in standard form. Thanks:)
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! For the linear equation in standard form 2x + 5y = 6:
:
a) Find the slope of this line:
Find the slope by putting the equation into the slope/intercept form y = mx + b
2x + 5y = 6:
5y = -2x + 6; subtracted 2x from both sides
y = -(2/5)x + (6/5)
Slope (m) = -2/5
:
b) Find the slope of a line parallel to this line
Parallel lines have equal slopes, therefore its slope = -2/5 also
:
c) Find the slope of a line perpendicular to this line
The relationship of slopes of perpendicular lines: m1*m2 = -1
-2/5 * m2 = -1
m2 = -1 * -5/2
m2 = +5/2 is the slope of a perpendicular line
:
d) use your answers to part c) to write the equation of the line which is perpendicular to the given line and passes through the point (-3,-4).
Use the point/slope form y - y1 = m(x - x1)
x1 = -3; y1 = -4; m = 5/2
y - (-4) = 5/2(x - (-3))
y + 4 = 5/2 (x + 3)
y + 4 = (5/2)x + 15/2
y = (5/2)x + 15/2 - 4
Y = (5/2)x + 15/2 - 8/2
y = (5/2)x + 7/2
:
Put final equation in standard form:
Multiply equation by 2 to get rid of the denominators
2y = 5x + 7; subtract 5x from both sides
-5x + 2y = 7; the standard form
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