To graph the equation $y = 2x + 3$, we follow these steps:

1. Identify the slope and y-intercept

• The equation is in the slope-intercept form, $y = mx + b$, where:
  • $m = 2$ is the slope.
  • $b = 3$ is the y-intercept.

2. Plot the y-intercept

• Start by plotting the point where the line crosses the y-axis. This happens when $x = 0$, so the point is $(0, 3)$.

3. Use the slope to find another point

• The slope is 2, which means for every 1 unit increase in $x$, $y$ increases by 2 units. So, from the point $(0, 3)$, move 1 unit to the right (increasing $x$ by 1) and then move up 2 units (increasing $y$ by 2). This gives us the point $(1, 5)$.

4. Draw the line

• Now that we have two points $(0, 3)$ and $(1, 5)$, draw a straight line passing through them. This is the graph of the equation $y = 2x + 3$.

Would you like to see the graph or need further explanation? Here are some related questions for your exploration:

1. How would you graph the equation $y = -3x + 1$?
2. What happens to the graph if the slope were 0 or undefined?
3. How do you find the x-intercept of a linear equation?
4. What is the relationship between slope and parallel or perpendicular lines?
5. How does the graph of $y = 2x + 3$ change if the equation becomes $y = 2x - 4$?

Tip: Always begin graphing a linear equation by identifying the y-intercept first, as this gives you a fixed starting point.