coordinate geometry – straight lines - The curve C has equation y= x^3 - 2x^2 - x +9,x 0 The point P has coordinates (2, 7). (a) Show that P lies on C.

Krishna (last edited 5 years ago) (Expert, Educator @Qalaxia)

Step 1: Note down the given data

Step 2: Plug the corresponding coordinates into the given equation and simplify

EXAMPLE: Given point (2, 16) and y = 7x + 2

x= 2, y = 16 substitute in the equation

7(2) + 2 = 16

14 + 2 = 16

16=16

Step 3: Verify that the statement is true statement or not

NOTE: If we get a true statement, such as 10 = 10. If we get something different, like 6 = 4, we know that the point is not on the line because it does not satisfy the equation.