Find the equation of the line through the points (5, 7) parallel to the line 7x + 5y = 12.

Find the equation of the line through the points (5, 7) parallel to the line 7x + 5y = 12.
A. 5x + 7y = 120
B. 7x + 5y = 70
C. x + y = 7
D. 15x + 17y = 90

Correct Option: Answer is B
Solution:

Equation through (5,7) parallel to the line
7x + 5y = 12
5y = 7x + 12
y = −7x/5+12/5
Gradient = −7/5
Required equation = (y-7)/(x-5) = (-7)/5
Cross multiply
Then you get 5y – 35 = -7x + 35
= 5y + 7x = 70

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