3 points on a line via eq. of line: Show that the following three points lie on a line:

(-4, 2); (-1, 1); (8, -2).

To solve this, we can determine the equation of the line through 2 of the points. Then we can test whether the coordinates of the 3^rd point satisfy the equation.

For the points (-4, 2) and (-1, 1) the definition of the slope gives

In the slope-intercept form, we get .

We can determine b by substituting one of the points. Using (-4, 2), we get , or b = 2/3. Consequently, the equation of the line through (-4,2) and (-1, 1) is .

Now we can test the coordinates of the third point (8, -2) to see if they satisfy this equation:

, and we see that the equation is satisfied. All three points satisfy the same equation of a line, and are on the same line.