The equation $y = 2x + 4$ is a linear equation representing a straight line in the coordinate plane. Here's a detailed breakdown:

Key Properties:

1. Slope ($m$): The coefficient of $x$, which is $2$. This means the line rises 2 units for every 1 unit it moves to the right.
2. Y-Intercept ($b$): The constant term $4$. This indicates the point where the line crosses the $y$-axis, at $(0, 4)$.
3. X-Intercept: This is the point where the line crosses the $x$-axis, which can be found by setting $y = 0$: $0 = 2x + 4 \implies x = -2$ So, the $x$-intercept is $(-2, 0)$.

Graphing the Line:

1. Plot the y-intercept at $(0, 4)$.
2. Use the slope $2$ to find another point. Starting at $(0, 4)$, move up 2 units and right 1 unit to reach $(1, 6)$.
3. Draw a straight line through these points, extending it in both directions.

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Questions for Exploration:

1. What happens to the graph if the slope is changed to a negative value, such as $y = -2x + 4$?
2. Can you find the equation of a line parallel to $y = 2x + 4$ passing through the origin?
3. How does the graph change if the y-intercept is reduced to $2$ (i.e., $y = 2x + 2$)?
4. What are the coordinates of three points that satisfy the equation $y = 2x + 4$?
5. How would you rewrite the equation in standard form $Ax + By = C$?

Tip:

To confirm the slope visually, choose two points on the line and calculate $\text{slope} = \frac{\Delta y}{\Delta x}$.