1. The problem is to find the value of $y$ when $x=2$ for the linear equation $y=2x+3$. 2. The formula given is $y=2x+3$, where $2$ is the slope and $3$ is the y-intercept. 3. Substitute $x=2$ into the equation: $$y=2(2)+3$$ 4. Simplify the expression: $$y=4+3=7$$ 5. Therefore, when $x=2$, the value of $y$ is $7$. This means the point $(2,7)$ lies on the line $y=2x+3$. The graph is a straight line with slope $2$ and y-intercept $3$, passing through $(0,3)$ and rising upwards to the right.