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 $y=\frac{3}{2}x+\frac{1}{2}$

Step-by-step explanation:

The slope of the line is

$\frac{-1-8}{-1-5}=\frac{-9}{-6}=\frac{3}{2}$

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

$y+1=\frac{3}{2}(x+1)\\\\y+1=\frac{3}{2}x+\frac{3}{2}\\\\y=\frac{3}{2}x+\frac{1}{2}$

Therefore, all points $(x,y)$ that satisfy $y=\frac{3}{2}x+\frac{1}{2}$ will lie on the same line.