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

`y+3=-4x`

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
2 hours ago

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.