Question

Ax+By=C form with slope of 14 over 13 with points (5,6) and (-8,-8)

Answer 1

`\displaystyle\\Answer:\ -(14)/(13) x+y=(8)/(13)`

Explanation:

Ax+By=C the slope is 14/13 (5,6) (-8,-8)

The slope m equil 14/13

`\displaystyle\\By=mx+C\\\\By=(14)/(13) x+C\ \ \ \ (1)`

Substitute the coordinates of the points into equation (1) and obtain a system of equations:

`\displaystyle\\\left \{ {{B(6)=(14)/(13)(5)+C } \atop {B(-8)=(14)/(13)(-8)+C }} \right.\\\\\left \{ {{6B=(70)/(13) +C\ \ \ \ \ \ \ (2)} \atop {-8B=-(112)/(13)+C\ \ \ (3) }} \right.`

Multiply both parts of the equation (3) by -1:

`\displaystyle\\\left \{ {{6B=(70)/(13)+C \ \ \ \ (4)} \atop {8B=(112)/(13)-C }} \right.`

Add these equations :

`14B=(182)/(14)\\\\ 14B=14`

Divide both parts of the equation by 14:

`B=1`

Hence, let's substitute the value of B into equation (4):

`\displaystyle\\6(1)=(70)/(13)+C \\\\6=(70)/(13)+C\\6-(70)/(13) =(70)/(13) +C-(70)/(13)\\\\(6*13-70)/(13)=C\\\\(78-70)/(13)=C\\\\(8)/(13)=C\\`

`\displaystyle\\Thus,\ C=(8)/(13)\\\\ So,\ 1(y)=(14)/(13) x+(8)/(13) \\ -(14)/(13) x+y=(8)/(13)`