Question

the rule for this line is y is $\frac{1}{2}$ less than x.which of these points are on the line?on the line not on the line$(11,10\frac{1}{2})$ $(2,1\frac{1}{2})$ $(1\frac{1}{2},2)$ $(11,2\frac{1}{2})$

Explanation:

Step1: Write line equation

The rule states $y = x - \frac{1}{2}$.

Step2: Test point $(11, 10\frac{1}{2})$

Substitute $x=11$: $y = 11 - \frac{1}{2} = 10\frac{1}{2}$. This matches the point.

Step3: Test point $(2, 1\frac{1}{2})$

Substitute $x=2$: $y = 2 - \frac{1}{2} = 1\frac{1}{2}$. This matches the point.

Step4: Test point $(1\frac{1}{2}, 2)$

Substitute $x=1\frac{1}{2}$: $y = 1\frac{1}{2} - \frac{1}{2} = 1$. This does not match 2.

Step5: Test point $(11, 2\frac{1}{2})$

Substitute $x=11$: $y = 11 - \frac{1}{2} = 10\frac{1}{2}$. This does not match $2\frac{1}{2}$.

Answer:

On the line:

$(11, 10\frac{1}{2})$, $(2, 1\frac{1}{2})$

Not on the line:

$(1\frac{1}{2}, 2)$, $(11, 2\frac{1}{2})$