Graph the line that contains the point (−2, −3) and has slope m =
4
3
. Don’t write an
equation, but use the definition of slope to make your graph.

To graph the line containing the point \((-2, -3)\) and with a slope of \(\frac{4}{3}\), we can use the definition of slope, which is:

\[
m = \frac{\text{rise}}{\text{run}}
\]

Here, the slope \(m = \frac{4}{3}\) means that for every 3 units you move horizontally (run), you move 4 units vertically (rise).

### Steps to graph the line:
1. **Start at the point** \((-2, -3)\) on the coordinate plane.
2. **From this point**, use the slope \(\frac{4}{3}\):
   - Move **3 units to the right** (positive direction on the x-axis).
   - Move **4 units up** (positive direction on the y-axis).
   
   After making these moves, you reach the point \((1, 1)\).
   
3. **Plot both points**: \((-2, -3)\) and \((1, 1)\).
4. **Draw a straight line** through these points to complete the graph.

Would you like me to plot this graph for you?

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Here are 5 related questions to expand on this:

1. How would the graph change if the slope was negative?
2. What if the line had to pass through a different point, like (0, 0)?
3. How can you calculate the y-intercept from the graph?
4. What if the slope was \(\frac{3}{4}\) instead of \(\frac{4}{3}\)?
5. How would the graph look if the slope was undefined?

**Tip**: When graphing lines, always plot a few points to ensure accuracy.

Graph the line that contains the point (−2, −3) and has slope m = 4/3. Don’t write an equation, but use the definition of slope to make your graph.

Learn how to graph a line that passes through the point (-2, -3) with a slope of 4/3 using the definition of slope. This problem covers key algebraic concepts related to graphing linear equations and slope calculation. Suitable for students in Grades 6-8.

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