Question

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).

Answer 1

tell me where to put it

Answer 2

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.

Answer 3

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!