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A map of the town that Hannah lives in can be represented by the Cartesian plane. Hannah starts off at (-4, 9) and walks 10 units to the left and 7 units down to get to her new location. Along what line could she have walked to get to the new location directly from her old location? Express your answer in the form ax + by = c where c is a positive integer and a and b are integers not having any common factors other than 1.

Logic  Aug 28, 2018
 #1
avatar+88775 
+1

(-4, 9)...   10  left  7 down  puts her at  (  -4 - 10 , 9  - 7)  = ( -14, 2)

 

So....  the points  ( -4, 9)  and (-14,2)  are on the  line

 

Slope of this line  =   [ 2 - 9] / [ -14 - -4 ]  =  [ -7] / [ -10]  =  7/10

 

Equation of the line

 

y  = (7/10)(x - - 4)  + 9

 

y  = (7/10) ( x + 4)  + 9     multiply through by 10

 

10y = 7 (x + 4)  + 90

 

10y = 7x + 28  + 90

 

-7x + 10y  = 118

 

Here's a graph : https://www.desmos.com/calculator/jlpnh4ai3p

 

 

cool cool cool

CPhill  Aug 28, 2018
 #2
avatar+149 
0

It didn't work?

Logic  Aug 28, 2018
 #3
avatar+88775 
0

What didn't work  ??

 

 

cool cool cool

CPhill  Aug 28, 2018

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