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USPshnik [31]
4 years ago
7

What is the equation of a line that is parallel to 4x+6y+5=0 and passes through the points (6,9)

Mathematics
1 answer:
OLga [1]4 years ago
4 0

Step-by-step explanation:

Equation of given line is:

4x+6y+5=0  \\  \therefore \: 6y =  - 4x - 5 \\ \\  \therefore \: y =  \frac{ - 4x - 5}{6}  \\   \\ \therefore \: y =  \frac{ - 4x}{6}  -  \frac{5}{6}  \\  \\  \therefore \: y =  -  \frac{ 2}{3}x  -  \frac{5}{6}...(1)  \\  equating \: eq \: (1) \: with \:   y = mx + c, \:we \:\\ find :  \\ slope \: of \: given \: line \: (m) = -  \frac{ 2}{3} \\  \because \: required \: line \: is \:  \parallel \: to \: given \: line \\  \therefore \: slope \: of \:  required \: line  \\  = slope \: of \: given \: line \: (m) = -  \frac{ 2}{3}  \\   \because \: required \: line  \: passes \: through \:  \\ point \: (6, \: 9) \\  \therefore \: \: equation \: of \: line \: in \: slope \: point \:  \\ form \: is \: given \: as:  \\ y-y_1=m(x-x_1) \\ \therefore \:y - 9 =  -  \frac{ 2}{3}(x - 6) \\ \therefore \:3(y - 9 )=  -  2(x - 6) \\ \therefore \:3y - 27=  -  2x  + 12 \\ \therefore \:2x + 3y - 27 - 12 = 0 \\  \purple{ \boxed{\therefore \:2x + 3y - 39 = 0}} \\ is \: the \: equation \: of \: required \: line

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