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what is the equation of a line through point (-4,5) that is perpendicular to the line with equality y=-6x+4?

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1 Answer

The slopes of perpendicular lines are negative reciprocals.  
 
The slope of the line y = -6x + 4 is -6.  So, any line perpendicular to that line has slope 1/6.
 
By the point slope form, an equation of the line with slope 1/6 and passing through the point (-4, 5) is:
 
y - 5 = (1/6)(x - (-4))
 
y - 5 = (1/6)x + 2/3
 
y = (1/6)x + 17/3