Question 1151104
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Call the coordinates of point P (0,b).<br>
Find the x intercept of a line with slope 3 passing through P(0,b):<br>
{{{(b-0)/(0-x) = 3}}}
{{{b/(-x) = 3}}}
{{{b = -3x}}}
{{{x = (-1/3)b}}}<br>
Find the x intercept of a line with slope -4 passing through P(0,b):<br>
{{{(b-0)/(0-x) = -4}}}
{{{b/(-x) = -4}}}
{{{b = 4x}}}
{{{x = (1/4)b}}}<br>
Use the fact that the two x-intercepts are 14 units apart to determine b.<br>
{{{(1/4)b-(-1/3)b = 14}}}
{{{(1/4)b+(1/3)b = 14}}}
{{{(7/12)b = 14}}}
{{{b = (12/7)*14 = 12*2 = 24}}}<br>
ANSWER: The distance of P from the origin is b = 24.<br>