Question

Equation of the line (-6,5) and (8,14) in standard form

Answer 1

`\huge\boxed{9x-14y=-70}`

Explanation:

The point-slope form of an equation of a line:

`y-y_1=m(x-x_1)\\\\m=(y_2-y_1)/(x_2-x_1)`

We have two points (-6, 5) and (8, 14).

Substitute:

`m=(14-5)/(8-(-6))=(9)/(14)\\\\y-5=(9)/(14)(x-(-6))\\\\y-5=(9)/(14)(x+6)`

Thew standard form of an equation of a line:

`Ax+By=C`

transform:

`y-5=(9)/(14)(x+6)\qquad|\text{multiply both sides by 14}\\\\14y-14\cdot5=14\!\!\!\!\!\diagup^1\cdot(9)/(14\!\!\!\!\!\diagup_1)(x+6)\\\\14y-70=9(x+6)\\\\14y-70=9x+54\qquad|\text{subtract}\ 9x\ \text{from both sides}\\\\-9x+14y-70=54\qquad|\text{add 70 to both sides}\\\\-9x+14y=70\qquad|\text{change the signs}\\\\9x-14y=-70`