Question

Find the x-intercept and the y-intercept of the graph of each equation. Then graph of the equation.

$y=x$

Short answer

The x-intercept of the given equation is $0$and the y-intercept is $0.$

Step-by-step solution

Step 1- Given information

A linear equation y=x.

Step 2- Concept used

The y-coordinate of the point at which a graph crosses the y-axis is called the y-intercept.

So, the y-intercept is the value of $y$ when$x=0.$

The x-coordinate of the point at which a graph crosses the x-axis is called the x-intercept.

So, the x-intercept is the value of $x$ when $y=0.$

Step 3- To find the x-intercept and y-intercept.

From the given information,

$\begin{array}{l}y=x\\ \Rightarrow x-y=0\left(1\right)\end{array}$

Substitute the $y=0$in the equation (1).

$\begin{array}{l}x-0=0\\ \Rightarrow x=0\end{array}$

Therefore, the x-intercept is$0$and the coordinate is

$\left(0,0\right).$

Now, substitute the $x=0$in the given equation (1).

$\begin{array}{l}0-y=0\\ \Rightarrow -y=0\\ \Rightarrow y=0\end{array}$

Therefore, the y-intercept is $0$ and coordinate is

$\left(0,0\right).$

Step 4- Graph of the of the given equation

The graph of the given equation is: