Question

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

Then plot the intercepts to graph the equation.

Keyboard Instructions
Initial graph state
The horizontal axis goes from -10.8 to 10.8 with ticks spaced every 1 unit(s).
The vertical axis goes from -10.8 to 10.8 with ticks spaced every 1 unit(s).

Answer 1

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.