Question

on which of the following lines does the point (1,6) lie

Answer 1

It is required to determine which line the point (1,6) lies on.

To do this, substitute the point into each equation and check which of the equations it satisfies.

Check the first equation:

$\begin{gathered} y=x+5 \\ \text{ Substitute }(x,y)=(1,6): \\ \Rightarrow6=1+5 \\ \Rightarrow6=6 \end{gathered}$

Since the equation is true, it follows that the point lies on the line.

Check the second equation:

$\begin{gathered} y=-x+7 \\ \text{ Substitute }(x,y)=(1,6): \\ \Rightarrow6=-1+7 \\ \Rightarrow6=6 \end{gathered}$

Since the equation is true, it follows that the point also lies on the line.

Check the third equation:

$\begin{gathered} y=2x-1 \\ \text{ Substitute }(x,y)=(1,6): \\ \Rightarrow6=2(1)-1 \\ \Rightarrow6=1 \end{gathered}$

Notice that the equation is not true. Hence, the point does not lie on the line.

So the given point only lies on lines a and b.

The answer is option D.