Question

Determine whether the given points are on the graph of the equation.

$x-2y-1=0;\left(0,0\right),\left(1,0\right),\left(-1,-1\right)$

Short answer

The points$\left(1,0\right)\text{and}\left(-1,-1\right)$ lie on the graph of the equation and the point$\left(0,0\right)$ does not lie on the graph of the equation.

Step-by-step solution

Step 1. Apply the concept of coordinates.

The set of all points$\left(x,y\right)$ in the Cartesian plane or coordinate plane that satisfy the equation is known as the graph of the equation in x and y coordinates.

Step 2. Substitute point and check.

Consider the provided set of points $\left(0,0\right),\left(1,0\right)\text{and}\left(-1,-1\right)$and equation of graph $x-2y-1=0$.

Recall that the set of all points $\left(x,y\right)$ in the Cartesian plane or coordinate plane that satisfy the equation is known as the graph of the equation in x and y coordinates.

Substitute the point $\left(0,0\right)$ in the equation $x-2y-1=0$ and check whether the left-hand side is equal to the right-hand side.

$$\begin{gathered} 0-2\left(0\right)-1=0 \\ -1=0 \end{gathered}$$

The above equality does not hold so, the point $\left(0,0\right)$does not lie on the graph of the equation.

Substitute the point $\left(1,0\right)$in the equation $x-2y-1=0$and check whether the left-hand side is equal to the right-hand side.

$$\begin{gathered} 1-2\left(0\right)-1=0 \\ 1-1=0 \\ 0=0 \end{gathered}$$

The above equality holds true so, the point $\left(1,0\right)$lie on the graph of the equation.

Substitute the point $\left(-1,-1\right)$in the equation $x-2y-1=0$and check whether the left-hand side is equal to the right-hand side.

role="math" localid="1643381994490" $$\begin{gathered} -1-2\left(-1\right)-1=0 \\ -1+2-1=0 \\ 0=0 \end{gathered}$$

The above equality holds true so, the point $\left(-1,-1\right)$lie on the graph of the equation.

Thus, the points $\left(1,0\right)\text{and}\left(-1,-1\right)$lie on the graph of the equation whereas the point $\left(0,0\right)$does not lie on the graph.

Step 3. Graph the equation.

Now, on the Cartesian plane graph the line$x-2y-1=0$ and verify.