alright...
we know line (c)'s equation which is y = -2x + 3 and we also know that line (c) is perpendicular to line (b) ...which means line (b)'s slope would be the
reciprocal of line (c)'s slope... we know line (c)'s slope is -2 which means line (b)'s slope will be 1/2.... we also know that line (b) goes through (3,1)...now we can easily find (b)'s equation
(y - 1) / (x - 3) = 1 / 2
simplifying this equation gives us.... 2y - 2 = x - 3 which comes out to y = 1x/2 - 1/2
now that we know the equation for line (b), we can easily find the equation of line (a), since line (a) is parallel to line (b) and we know line (a) goes through (1,2) , ... using the same process...
(y - 2) / (x - 1) = 1/2
2(y - 2) = 1(x - 1)
2y - 4 = x - 1
2y = x + 3
y = 1x/2 + 3/2
now that we know what line (a)'s equation is, we can now find the y-intercept of line (a)
y = (0)/2 + 3/2 = y = 3/2
therefore the y-intercept for line (a) is (3/2)
I hope this helps....
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