Which graph represents y = 2x + 1?

To represent the equation y = 2x + 1 on a graph, we are looking for a straight line because this is a linear equation.

The graph of this equation can be sketched by plotting points that are solutions to the equation and then drawing a line through them. Here is a step-by-step method to plot the graph:

1. Start with the y-intercept. The y-intercept is the value of y when x is zero. For the equation y = 2x + 1, when x is 0, y is 1. So we have the point (0,1) on the y-axis.

2. Use the slope to find another point. The number 2 in the equation is the slope (m), which is the change in the y-value divided by the change in the x-value between two points on the line. A slope of 2 means that for every 1 unit we move to the right on the x-axis, we move up 2 units on the y-axis.

3. If we start at the y-intercept (0,1) and follow the slope, we move one unit to the right (x = 1) and two units up (y = 3). That gives us a second point: (1,3).

4. Plot both points, (0,1) and (1,3), on the graph.

5. Draw a straight line that passes through both points. Extend the line across the graph, and you'll have a graphical representation of y = 2x + 1.

6. Make sure the line is straight and extends in both positive and negative directions beyond the plotted points, as the linear equation continues infinitely in both directions.

If given multiple graphs to choose from, you would pick the graph that shows a straight line crossing the y-axis at 1 with a slope that rises 2 units for every 1 unit it moves to the right. The slope should be positive, indicating that the line slants upward from left to right.