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Question 992766: Find an equation of the line that satisfies the given conditions(a) write the equation in slope-intercept form(b) write the equation in standard form. Through(4,1) parallel to 2x+5y=10
Through (2,-7) perpendicular to 5x+2y=18
Answer by Cromlix(4381)   (Show Source):
You can put this solution on YOUR website! Hi there,
Through(4,1) parallel to 2x+5y=10
Sort 2x + 5y = 10 into:-
y = mx + c form
5y = -2x + 10
y = -2/5x + 2
Gradient (m) = -2/5
Lines that are parallel to one another
have gradients that equal one another.
m1 = m2
Using line equation:-
y - b = m(x - a)
m = -2/5 (a,b) = (4,1)
y - 1 = -2/5( x - 4)
y - 1 = -2/5x + 8/5
y = -2/5x + 8/5 + 5/5 (1)
y = -2/5x + 13/5
or
5y = -2x + 13
..................
Through (2,-7) perpendicular to 5x+2y=18
Sort 5x + 2y = 18 into:-
y = mx + c form
2y = -5x + 18
y = -5/2x + 9
Gradient (m) = -5/2
Lines that are parallel to one another
have gradients that multiply together
to give -1
m1 x m2 = -1
-5/2 x m2 = -1
m2 = 2/5
Using line equation:-
y - b = m(x - a)
m = 2/5 (a,b) = (2,-7)
y - (-7) = 2/5(x - 2)
y + 7 = 2/5x - 4/5
y = 2/5x - 4/5 - 35/5 (7)
y = 2/5x - 39/5
or
5y = 2x - 39
Hope this helps :-)
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