Does this Point Lie on The Line?

How do you know if a point lies on a given line? For example, does the point (1, 2) lie on the line 3x + y = 7? If you graph the line and the point on the same grid, you will see that the point does not lie on the line.

There are two ways to check if a point lies on a line:
1) Graph the line and the point as we did above; or
2) Use algebra to check if the point satisfies the equation of the line.

Example 1: Does the point (5, -3) lie on the line (y + 1) = 2(x - 6)? Do not use graphing.

Solution: Since every point on the line (y + 1) = 2(x - 6) must satisfy this equation, you can just substitute the values (5, -3) into the equation to check if the point lies on the line.

Since the left hand side of the equation equals the right hand side, the point (5, -3) lies on the line y = 2x - 13.

Example 2: The local used record store is having a sale. You pay $15.00 for the first CD and only $5.00 for every additional CD. The sale can be represented by the line y = 5x + 10, where x is the number of CDs you bought and y is the amount of money you spent. Your friend Joey says that you can buy 15 CDs with $75. Is he right?

Solution: Joey says that you can get 15 CDs for $75. Since x is the number of CDs and y is the cost, Joey is also saying that the point (15, 75) lies on the line y = 5x + 10. Does it?

Since the left hand side of the equation does not equal the right hand side, the point (15, 75) isn't on the line y = 5x + 10. Your friend Joey is wrong. You need to pay $85 to get 15 CDs. How many CDs can you buy for $75?