Question 1183832
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When you digest the given information, you will find that the problem is asking whether the closest point on the line y=5x-4 is more than 2 units from the origin.<br>
The the distance from a point (p,q) to the line Ax+By+C=0 (i.e., the shortest distance from (p,q) to any point on the line) is given by this formula:<br>
{{{abs((Ap+Bq+C)/sqrt(A^2+B^2))}}}<br>
Changing the form of the equation of the line to the required form, we get 5x-y-4=0.  Then plugging the appropriate numbers in the formula gives the distance from the origin to Michael's house as<br>
{{{abs(((5*0)+(1*0)+4)/sqrt(5^2+1^2)) = 4/sqrt(26)}}}<br>
That is less than 1 mile...<br>
ANSWER: No, Michael does not live far enough away from his school to qualify for getting bus service.<br>
Even a rough sketch of the line with equation y=5x-4 shows that the shortest distance from the origin to the line is far less than 2; in fact it is clearly less than 1:<br>
{{{graph(400,400,-2,4,-10,4,5x-4)}}}<br>