The equation you are asked to graph is $y = 2x + 3$.

This is a linear equation in slope-intercept form, $y = mx + b$, where:

• $m = 2$ is the slope, meaning that for every 1 unit increase in $x$, $y$ increases by 2 units.
• $b = 3$ is the y-intercept, meaning the line crosses the y-axis at $y = 3$.

Steps to graph:

1. Plot the y-intercept (0, 3): Start by placing a point at $(0, 3)$, where the line crosses the y-axis.
2. Use the slope to find another point: The slope is 2, which means for every 1 unit you move right along the x-axis, you move 2 units up. From the point $(0, 3)$, move 1 unit to the right and 2 units up to plot the point $(1, 5)$.
3. Draw the line: Connect the two points $(0, 3)$ and $(1, 5)$ with a straight line. You can extend this line in both directions for a more complete graph.

Would you like more details on graphing linear equations, or do you have any specific questions?

Here are 5 related questions for further practice:

1. What does the slope of the line represent in this context?
2. How would the graph change if the equation was $y = -2x + 3$?
3. What is the x-intercept of the equation $y = 2x + 3$?
4. How can you determine the slope of a line given two points on the graph?
5. How would the equation change if the subway fare had an initial fee of $4 instead of $3?

Tip: When graphing lines, always identify the slope and intercept first to make plotting points easier!