1. The problem is to find the value of $y$ when $x=2$ for the linear equation $y=2x+3$. 2. Substitute $x=2$ into the equation: $$y=2(2)+3$$ 3. Simplify the expression: $$y=4+3=7$$ 4. Therefore, when $x=2$, the value of $y$ is $7$. 5. The graph of the equation $y=2x+3$ is a straight line with slope $2$ and y-intercept $3$. It crosses the y-axis at $(0,3)$ and rises 2 units for every 1 unit it moves to the right.