The equation of the line that is perpendicular to the line whose equation is 2y=3x-10 and passes through (-6,1) is; y - 1 = (-2/3)x - 4
We are given the equation of a line as;
2y = 3x - 10
Rewriting in slope intercept form gives us;
y = (3/2)x - 10
where;
slope; m = 3/2
Now, we are told that an equation is perpendiclar to the above and passes through the point (-6, 1).
Thus;
New slope = -1/(3/2) = -2/3
Thus;
New equation is; y - 1 = (-2/3)(x + 6)
y - 1 = (-2/3)x - 4
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