Answer:

To graph the equation \(y = x + 3\) using \(x\)- and \(y\)-intercepts, we need to find the points where the line intersects the \(x\)- and \(y\)-axes.

To find the \(x\)-intercept, we set \(y\) to zero and solve for \(x\):

\[

0 = x + 3

\]

Subtracting 3 from both sides, we get:

\[

-3 = x

\]

So the \(x\)-intercept is \((-3, 0)\).

To find the \(y\)-intercept, we set \(x\) to zero and solve for \(y\):

\[

y = 0 + 3

\]

Simplifying, we find that the \(y\)-intercept is \((0, 3)\).

Now we can plot these intercepts on a coordinate plane:


The blue line represents the graph of the equation \(y = x + 3\), passing through the \(x\)-intercept \((-3, 0)\) and the \(y\)-intercept \((0, 3)\).