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# Algebra help!

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Tina the tourist goes on a trip. She starts at the origin and drives north (in the positive \$y\$ direction) for \$10\$ units. Then she turns east (the positive \$x\$ direction) and as she's turning her camera flies out the window and lands exactly at \$(0,10)\$. She then drives \$9\$ units east, turns and drives \$8\$ units north. She continues this pattern of turning and driving one unit less than after the previous turn, until stopping after driving \$1\$ unit east. She reaches for her camera only to find it missing! She activates the GPS homing device on her camera and drives back to it in a straight line. What is the equation of this line? Express your answer as \$ax+by=c\$, where \$a\$, \$b\$, and \$c\$ are integers, \$a>0\$, and \$a\$ is as small as possible.

Apr 4, 2019

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Consider where her camer flew out as the 'origin' of her troubles.... she travels  9+ 7+5+3+1 east from there (25 mi)

and she travels 8+6+4+2 north = 20 mi

y= mx+b    m = slope = rise / run = 20/25 = 4/5

y = 4/5 x + b     and passes through the point   0,10

10 = 4/5 (0) + b

b =10

y = mx+ b becomes

y = 4/5 x + 10      or     y - 4/5 x = 10      or   5y - 4x = 50  or      4x-5y=-50    for the form required

Apr 4, 2019