a Substitute the coordinates of the points into the given formula and check whether the result is a true statement.
B
b Substitute the coordinates of the points into the given formula and check whether the result is a true statement.
A
a Points X and Y lie on the line, Z does not.
B
b Points Y and Z lie on the line, X does not.
Practice makes perfect
a In order to check whether a point lies on the given line, we need to substitute its coordinates into the formula for the line and check if the result is a true statement. Let's start with point X( 0, 15).
Since the result is a true statement, we know that X lies on the given line. Let's check the other two points in a similar fashion.
Point
y ? = 1/3x + 15
Equality?
On the line?
X( 0, 15)
15 ? = 1/3( 0)+15
15=15 ✓
Yes
Y( 3, 16)
16 ? = 1/3( 3) + 15
16 = 16 ✓
Yes
Z( 7, 0)
0 ? = 1/3( 7) + 15
0 ≠17 13 *
No
As we can see, X and Y lie on the given line, but Z does not.
b In order to check whether a point lies on the given line, we need to substitute its coordinates into the formula for the line and check if the result is a true statement. Let's start with point X( 0, 15).
