Question

graph the line that passes through the point (-1,-4) and whose slope is -2

Answer 1

To graph the line that passes through the point (-1, -4) with a slope of -2, you can use the point-slope form of the linear equation, which is:

\[
y - y_1 = m(x - x_1)
\]

where \(m\) is the slope and \((x_1, y_1)\) is the point the line passes through. In this case, \(m = -2\), \(x_1 = -1\), and \(y_1 = -4\).

Plugging in these values, we get:

\[
y - (-4) = -2(x - (-1))
\]

Simplifying this, we have:

\[
y + 4 = -2(x + 1)
\]
\[
y + 4 = -2x - 2
\]
\[
y = -2x - 2 - 4
\]
\[
y = -2x - 6
\]

Now we have the equation of the line:

\[
y = -2x - 6
\]

### Steps to Graph:

1. **Plot the point (-1, -4)** on the graph.
2. **Use the slope** of -2, which can be expressed as -2/1. This means that for every 1 unit you move to the right (positive direction along the x-axis), you move down 2 units (negative direction along the y-axis).
3. **From (-1, -4)**:
- Move 1 unit to the right to get to \(0\) on the x-axis, and then move down 2 units to \( -6\). This gives you the next point, \( (0, -6) \).
4. You can continue using the slope to plot additional points if needed, or draw a straight line through the points (-1, -4) and (0, -6).

### Line Visualization:

Now, you can draw a line through the points you've plotted. Make sure to extend the line in both directions and label it with the equation \(y = -2x - 6\).

This will give you the graph of the line.