To sketch a line that passes through the point [tex]\((2, -3)\)[/tex] with a slope [tex]\(m = -\frac{3}{5}\)[/tex], follow these steps:
1. Identify the point and the slope:
- The point is [tex]\((2, -3)\)[/tex].
- The slope [tex]\(m = -\frac{3}{5}\)[/tex] means that for every 5 units you move to the right along the x-axis, you move 3 units down along the y-axis (because of the negative sign).
2. Plot the given point:
- Locate and plot the point [tex]\((2, -3)\)[/tex] on the graph.
3. Use the slope to find a second point:
- Starting from [tex]\((2, -3)\)[/tex], move 5 units to the right along the x-axis. After moving 5 units to the right from [tex]\(x = 2\)[/tex], you will be at [tex]\(x = 2 + 5 = 7\)[/tex].
- From [tex]\(x = 7\)[/tex], move 3 units down along the y-axis. After moving 3 units down from [tex]\(y = -3\)[/tex], you will be at [tex]\(y = -3 - 3 = -6\)[/tex].
- So, the second point is [tex]\((7, -6)\)[/tex].
4. Plot the second point:
- Locate and plot the point [tex]\((7, -6)\)[/tex] on the graph.
5. Draw the line:
- Using a ruler or straight edge, draw a line through the points [tex]\((2, -3)\)[/tex] and [tex]\((7, -6)\)[/tex]. Extend the line in both directions to cover the entire graph.
By following these steps, you have successfully sketched the line passing through the point [tex]\((2, -3)\)[/tex] with a slope of [tex]\(-\frac{3}{5}\)[/tex].
