suppose that someone has said that the equation connecting points ((-1,1) and (2,3) is y= 2/3x + 5/3. This person wants to know whether the line represented by this will contain point (6,9). Identify two ways by which this person can decide whether the graph of the equation contains the point.
I would first check if the line actually passes through the given points before we look at the third point.
To check if the line passes through the third point, we substitute the x-value (6) into the right hand side of the equation and evaluate. If the result corresponds to the y-value of 9, then the line passes trough the point.
In fact, you do the same procedure to check if the line passes through the two initial points.
a second method : would be to find the slope of the line between the third point and one of the first two points. If it equals (2/3), the slope of the given line, then the line passes through the third point.