Which point is collinear with the points (3,-5),(2,-3),and (-1,3)

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mr-mayonnaise eNotes educator| Certified Educator

Points are said to be collinear if they lie on the same straight lines as shown on a graph. These points also are connected by the same relationship or ratio. This can be found using the slope equation m = (y2-y2/x2-x2)

`m = (y_2 - y_1)/(x_2 - x_1)`


`m= 2/-1 = -2`

Putting this into slope-intercept form (y=mx+b) gives us the line that all collinear points can be found on. By graphing the line using the above points, we find that the y-intercept is 1.


`y= -2*x+1`

If you plot these points on a graph you can find a line that descends at the required ratio to show all collinear points. 

Collinear points includes: (0,1), (1,-1), (-2, 5) and so on. As long as the coordinates fulfill the above slope-intercept equation the point can be considered collinear! 

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