# How do you determine whether (3,-1) is on the line y=1/3x+5?

May 27, 2017

The given point does not make the equation true, therefore it does NOT lie on the line.

#### Explanation:

The co-ordinates you are given $\left(3 , - 1\right)$ consist of $x \mathmr{and} y$.

Remember that the line is represented by an EQUATION, which means that the left side and the right side must be equal.

If the given point IS on the line, then the $x \mathmr{and} y$ values will make the equation TRUE.

If the given point IS NOT on the line, then the $x \mathmr{and} y$ values will not work for the equation and your answer will be FALSE.

Substitute $x \mathmr{and} y$ into the equation and simplify:

$y = \frac{1}{3} x + 5$

$- 1 = \frac{1}{3} \left(3\right) + 5$

$- 1 = 1 + 5$

$- 1 = 6 \text{ } \leftarrow$ FALSE!

$\therefore$ the point does NOT lie on the line.