The equation of the line parallel to the line y = 7/6x - 4 be,
7x - 6y + 5 = 0.
Given, an equation of a line
y = 7/6x - 4
we have to find the equation of a new line which is parallel to the given line y = 7/6x - 4
Let, the line pass through a point (1 , 2)
if the required line is parallel to the line y = 7/6x - 4
then, the slope of the line will also be,
m = 7/6
To get the equation of the line, we use slope-intercept form
(y - 2)/(x - 1) = 7/6
6(y - 2) = 7(x - 1)
6y - 12 = 7x - 7
7x - 6y - 7 + 12 = 0
7x - 6y + 5 = 0
So, the equation of the line parallel to the line y = 7/6x - 4 be,
7x - 6y + 5 = 0.
Hence, the equation of the required line be, 7x - 6y + 5 = 0
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