3 points not on a line via eq. of line: Determine whether the following three points lie on a line:

(-5, -3); (-2, 1); (7, 8).

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 (-5, -3) and (-2, 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 (-2, 1), we get , or b = 11/3. Consequently, the equation of the line through (-5, -3) and (-2, 1) is .

Now we can test the coordinates of the third point (7, 8) to see if they satisfy this equation:

Substituting 7, we get , which is not equal to the y coordinate of 8, and we see that the equation is not satisfied. This means that the point (7, 8) does not lie on the line determined by the other two points.