Question

Identify the slope and y intercept. Then, graph the linear equation.

`y+3=-4x`

Answer 1

To identify the slope and y-intercept from the given equation \( y + 3 = -4x \), we first need to get the equation into the slope-intercept form, which is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

1. **Isolate \( y \)**:
\[
y + 3 = -4x
\]
Subtract 3 from both sides:
\[
y = -4x - 3
\]

Now, we can identify the slope and y-intercept:
- The slope \( m = -4 \)
- The y-intercept \( b = -3 \)

### Graphing the Equation

To graph the equation \( y = -4x - 3 \):

1. **Plot the y-intercept**:
- The y-intercept is the point where the line crosses the y-axis. Here, it is \( (0, -3) \).

2. **Use the slope to find another point**:
- The slope \( -4 \) can be expressed as \( -4/1 \). This means that for every 1 unit you move to the right on the x-axis, you move 4 units down on the y-axis.
- Starting from the y-intercept \( (0, -3) \):
- Move 1 unit to the right to \( x = 1 \)
- Move 4 units down to \( y = -3 - 4 = -7 \)
- This gives us the point \( (1, -7) \).

3. **Plot the second point**:
- Plot the point \( (1, -7) \).

4. **Draw the line**:
- Connect these points with a straight line, extending it in both directions.

Here’s a summary of the points:
- Y-intercept: \( (0, -3) \)
- Another point: \( (1, -7) \)

### Graph Description

The graph is a straight line that slopes downward from left to right (due to the negative slope). The line crosses the y-axis at \( -3 \).

If you'd like a visual representation, you can use graph paper or graphing software to plot the points and the line.