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 Oct 9, 2019

#3**+3 **

Hannah starts at (-4, 9) walks 10 units to the left and then 7 units down

So.....she ends up at ( -4 -10 , 9 - 7) = (-14, 2)

So....we need to find the slope between (-4,9) and ( -14, 2)

We have

[ 2 - 9 ] / [ -14 - - 4] = [-7]/ [-10] =7/10

Using either of the points to write an equation of the line we have that

y =(7/10)(x - -4) + 9 simplify

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

10y = 7(x + 4) + 90

10y = 7x +28 + 90

10y = 7x + 118 subtract 7x from both sides

-7x + 10y = 118

CPhill Oct 9, 2019