The equation that represents a line that is perpendicular to the line MN is y = 4x - 6 , the correct option is (d) .
In the question ,
it is given that ,
the required line is perpendicular to the the given line .
we can see that the line MN passes through the point M(-7,6) and N(5,3) .
so , the slope will be = (3-6)/(5+7) = -3/12 = -1/4.
the slope of the perpendicular will be = 4 .
on comparing the the options with the equation of line y = mx + d, we get
that only option(d) has slope 4 .
So , the equation of the perpendicular is ⇒ y = 4x - 6 .
Therefore , the equation of the required line is y = 4x - 6.
The given question is incomplete , the complete question is
Which equation represents a line that is perpendicular to line MN ?
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