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Plot the x- and y-intercepts to graph the equation.



y=−12x−3

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).

3 answers

To graph the equation \( y = -12x - 3 \) and find the x- and y-intercepts, we will follow these steps:

1. Finding the y-intercept:

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

Substituting \( x = 0 \) into the equation: \[ y = -12(0) - 3 = -3 \] So the y-intercept is (0, -3).

2. Finding the x-intercept:

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

Setting \( y = 0 \) in the equation: \[ 0 = -12x - 3 \] Solving for \( x \): \[ 12x = -3 \ x = -\frac{3}{12} \ x = -\frac{1}{4} \] So the x-intercept is \((-0.25, 0)\).

3. Plotting the intercepts:

Now, let's plot the intercepts on the graph:

  • Y-intercept: (0, -3)
  • X-intercept: (-0.25, 0)

4. Sketch the line:

Next, we can draw the line that connects these two points. Since the slope of the line is -12 (indicating a steep downward slope), you can enjoy a visualization whenever you have the intercepts plotted.

Graph Visualization Instructions:

  1. Draw the horizontal and vertical axes.
  2. Mark the point (0, -3) on the y-axis.
  3. Mark the point (-0.25, 0) on the x-axis.
  4. Draw a line through these points, extending it in both directions.

Your graph should show a downward slope starting from the y-intercept towards the x-intercept. The orientation of points in relation to the provided limits on both axes should comply with the mentioned graphing instructions.

tell me where to put it

Certainly! Here's how to plot the x- and y-intercepts on your graph step-by-step:

Graph Setup

  1. Horizontal Axis (X-axis):

    • Range: from -10.8 to 10.8
    • Ticks: every 1 unit

  2. Vertical Axis (Y-axis):

    • Range: from -10.8 to 10.8
    • Ticks: every 1 unit

Plotting Points

  1. Plot the Y-Intercept (0, -3):

    • Move to the vertical (Y-axis) line and from the origin (0,0), go down to -3.
    • Mark the point (0, -3).

  2. Plot the X-Intercept (-0.25, 0):

    • Move to the horizontal (X-axis) line.
    • Find -0.25, which is slightly to the left of 0 (between -0.2 and -0.3).
    • Mark the point (-0.25, 0).

Drawing the Line

Once you have the points marked:

  • Draw a straight line that passes through both points:
    • The line should extend in both directions.

Final Note

  • Ensure your line is steep due to the slope of -12, meaning it will fall quickly as you move from left to right.

Here’s a visual representation of where to place the points:

  • Y-intercept: (0, -3) on the Y-axis (down from the origin).
  • X-intercept: (-0.25, 0) on the X-axis (slightly left of the origin).

By following the above instructions, you should be able to accurately represent the equation \( y = -12x - 3 \) on your graph!