Hi

Note: the standard slope-intercept form for an equation of a line is y = mx + b  

where m is the slope and b the y-intercept.  

line through A(3,1) perpendicular to x - 4y = 8 OR y = (1/4)x - 2  

Perpendicular lines have slopes that are negative reciprocals of one another

New line y = -4x + b using ordered pair Pt(3,1) to solve for b

         1 = -12 + b     b = 13

         y = -4x + 13   P(13/4,0) and Q(0,13)on this line

Calculate the ratio PA : AQ

PA Distance would be: P(13/4,0)and A(3,1)



PA = 

AQ Distance would be: A(3,1)and Q(0,13)

AQ =  

PA:AQ would be   1.031:12.369



 

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