Question

A line passes through the points (-1,-1) and (5,8) which points lie on the same line?

Answer 1

Answer: all points
`(x,y)` that satisfy
`y=(3)/(2)x+(1)/(2)`

Explanation:

The slope of the line is

`(-1-8)/(-1-5)=(-9)/(-6)=(3)/(2)`

So, substituting into point-slope form, the equation is

`y+1=(3)/(2)(x+1)\\\\y+1=(3)/(2)x+(3)/(2)\\\\y=(3)/(2)x+(1)/(2)`

Therefore, all points
`(x,y)` that satisfy
`y=(3)/(2)x+(1)/(2)` will lie on the same line.