Question

Show me a graph that has the point negative one and -2 and the slope of 1/3

Answer 1

Although I can't create visual graphs directly, I can guide you through how to plot the points and line with the specified slope.

1. **Identify the Point**: You are starting with the point \((-1, -2)\).

2. **Determine the Slope**: The slope is \(\frac{1}{3}\), which means for every 1 unit you move up (in the y-direction), you will move 3 units to the right (in the x-direction).

3. **Plot the Given Point**: On a Cartesian plane, locate the point \((-1, -2)\) which is 1 unit left and 2 units down from the origin.

4. **Using the Slope to Find Another Point**:
- From \((-1, -2)\), move up 1 unit (to \((-1, -1)\)) and then move 3 units to the right to \((2, -1)\).

5. **Plot the New Point**: Plot the point \((2, -1)\).

6. **Draw the Line**: Draw a straight line through the points \((-1, -2)\) and \((2, -1)\). This line will have a slope of \(\frac{1}{3}\).

7. **Equation of the Line**: You can also find the equation of the line using the point-slope form:
\[
y - y_1 = m(x - x_1)
\]
Plugging \((-1, -2)\) for \((x_1, y_1)\) and \(\frac{1}{3}\) for \(m\):
\[
y + 2 = \frac{1}{3}(x + 1)
\]
Simplifying this gives:
\[
y = \frac{1}{3}x - \frac{5}{3}
\]

If you have graphing software or a graphing calculator, you can input the point and the slope to visualize it easily!