The problem asks you to graph the equation $y = 2x + 4$ by plotting three points. Let’s analyze and solve step-by-step.

Steps to Solve:

1. The equation $y = 2x + 4$ is in slope-intercept form: $y = mx + b$, where:

   • $m = 2$ (the slope)
   • $b = 4$ (the y-intercept).

2. To graph this line, start by plotting the y-intercept (0, 4). This is where the line crosses the y-axis.

3. Use the slope $m = 2$, which means "rise over run" ($\text{rise} = 2$, $\text{run} = 1$):

   • From $(0, 4)$, move up 2 units and right 1 unit to get the next point $(1, 6)$.
   • From $(1, 6)$, repeat the process to get $(2, 8)$.

4. Alternatively, choose values for $x$, substitute them into the equation $y = 2x + 4$, and solve for $y$:

   • For $x = 0$, $y = 2(0) + 4 = 4$ → Point: $(0, 4)$
   • For $x = 1$, $y = 2(1) + 4 = 6$ → Point: $(1, 6)$
   • For $x = -1$, $y = 2(-1) + 4 = 2$ → Point: $(-1, 2)$

Correct Points:

The three points you can plot are:

1. $(0, 4)$
2. $(1, 6)$
3. $(-1, 2)$

Plotting:

1. Place the points $(0, 4)$, $(1, 6)$, and $(-1, 2)$ on the graph.
2. Draw a straight line through the points.

Would you like a graphical example or further clarification?

Relative Questions:

1. What does the slope $m = 2$ represent in this equation?
2. How would the graph change if the slope was negative (e.g., $y = -2x + 4$)?
3. How do you find the x-intercept of this line?
4. What happens to the graph if you change the $b$-value (e.g., $y = 2x + 6$)?
5. Can you write the equation of a line parallel to $y = 2x + 4$?

Tip:

Always double-check points by substituting back into the equation to avoid errors!