Determine the x- and y-intercepts of the graph of x+2y=−4 .

To determine the x- and y-intercepts of the equation \( x + 2y = -4 \), we'll follow these steps:

Finding the X-intercept

The x-intercept occurs when \( y = 0 \).

1. Set \( y = 0 \) in the equation: \[ x + 2(0) = -4 \implies x = -4 \]

So, the x-intercept is \( (-4, 0) \).

Finding the Y-intercept

The y-intercept occurs when \( x = 0 \).

1. Set \( x = 0 \) in the equation: \[ 0 + 2y = -4 \implies 2y = -4 \implies y = -2 \]

So, the y-intercept is \( (0, -2) \).

Summary of Intercepts

• X-intercept: \( (-4, 0) \)
• Y-intercept: \( (0, -2) \)

Plotting the Intercepts

To graph the equation \( x + 2y = -4 \):

1. Start by plotting the x-intercept at the point \( (-4, 0) \).
2. Then plot the y-intercept at the point \( (0, -2) \).

Drawing the Line

Once the points are plotted, draw a straight line through these two points. The line will extend infinitely in both directions, representing the equation \( x + 2y = -4 \).

The graph should appear as a straight line sloping downward from left to right.

If using graphing software or physically plotting, make sure you label your axes and mark the intercepts clearly.