The question asks to determine the x- and y-intercepts of the line given by the equation $2x + y = 4$, and then to graph the line. Let's go through each part step-by-step.

Step 1: Finding the Intercepts

1. X-Intercept: This is the point where the line crosses the x-axis, so $y = 0$.

   • Substitute $y = 0$ into the equation $2x + y = 4$: $2x + 0 = 4 \Rightarrow 2x = 4 \Rightarrow x = 2$
   • Therefore, the x-intercept is $(2, 0)$.

2. Y-Intercept: This is the point where the line crosses the y-axis, so $x = 0$.

   • Substitute $x = 0$ into the equation $2x + y = 4$: $2(0) + y = 4 \Rightarrow y = 4$
   • Therefore, the y-intercept is $(0, 4)$.

Step 2: Graphing the Line

To graph the line, you would plot the two intercepts:

• Plot the x-intercept at $(2, 0)$.
• Plot the y-intercept at $(0, 4)$.

Draw a straight line through these two points, as this line represents all points $(x, y)$ that satisfy the equation $2x + y = 4$.

Would you like me to provide a detailed graph for visualization?

Additional Questions

1. What is the slope of the line $2x + y = 4$?
2. How would the graph change if the equation were $2x + y = 6$ instead of $2x + y = 4$?
3. Can you express $2x + y = 4$ in slope-intercept form?
4. How do you find the intercepts for a line given in a different form, like $y = 3x + 1$?
5. What is the significance of the x- and y-intercepts in real-world applications?

Tip

For linear equations, remember that finding the intercepts is often a quick way to sketch the line without needing to plot many points.