1. **State the problem:** We want to graph the linear equation $y = 2x + 5$. 2. **Understand the formula:** This is a linear equation in slope-intercept form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. 3. **Identify slope and intercept:** Here, the slope $m = 2$ and the y-intercept $b = 5$. 4. **Plot the y-intercept:** Start by plotting the point $(0, 5)$ on the y-axis. 5. **Use the slope to find another point:** The slope $2$ means rise over run is $2/1$. From $(0,5)$, go up 2 units and right 1 unit to reach $(1,7)$. 6. **Draw the line:** Connect the points $(0,5)$ and $(1,7)$ with a straight line extending in both directions. 7. **Check with given points:** The points $(-10,-15)$, $(-5,-5)$, $(0,5)$, and $(5,15)$ lie on this line, confirming the graph is correct. This is how you graph the line $y = 2x + 5$ step-by-step.