Question

Points P(5, 7) and Q(-1, 1) lie on the graph of y = x + 2.

Determine whether each point is collinear with P and Q.
5. R(1, - 1)
6. S(-3, -1)​

Answer 1

R is not collinear.

S is collinear.

Explanation:

The equation of the graph is given by y =x +2 ........ (1).

Now, the points P and Q having coordinates (5,7) and (-1,1) respectively lie on the graph of the equation (1) because those points satisfy the equation.

Now, if we consider another point R having coordinates (1,-1), then it does not lie on the graph of equation (1) as it does not satisfy the equation.{If you put x=1, then y will be 3 but not -1}

Therefore, P, Q, R are not collinear. (Answer)

Again if we consider the point S(-3,-1), it satisfies equation (1).{If you put x=-3 in the equation (1), y will be -1}.

Therefore, P, Q, and S lie on the same straight line. and they are collinear. (Answer)