Question

What is the equation of the line that passes through (3, 5) and (-7, -6)?

Answer 1

the equation of the line is `11x-10y+17=0`

Explanation:

the given two points are: `(x_1,y_1)=(3,5)`
`(x_2,y_2)=(-7,-6)`

the slope is `m=(y_2-y_1)/(x_2-x_1)=(-6-5)/(-7-1)=(-10)/-11=10/11`
the equation of a line passing through 2 points is
`(y-y_1)=(y_2-y_1)/(x_2-x_1)(x-x_1)`
`(y-5)=11/10(x-3)`
`10(y-5)=11(x-3)`
`11x-10y+17=0`