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**+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

CPhill Aug 28, 2018