To determine which pair of points may describe a line with a slope of [tex]\(-\frac{5}{3}\)[/tex], we need to calculate the slope for each given pair of points and compare the result.
The formula to calculate the slope [tex]\(m\)[/tex] between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Let's calculate the slope for each pair of points:
1. For the points [tex]\((12, 13)\)[/tex] and [tex]\((17, 10)\)[/tex]:
[tex]\[ m_1 = \frac{10 - 13}{17 - 12} = \frac{-3}{5} = -0.6 \][/tex]
2. For the points [tex]\((16, 15)\)[/tex] and [tex]\((13, 10)\)[/tex]:
[tex]\[ m_2 = \frac{10 - 15}{13 - 16} = \frac{-5}{-3} = 1.666 \][/tex]
3. For the points [tex]\((0, 7)\)[/tex] and [tex]\((3, 10)\)[/tex]:
[tex]\[ m_3 = \frac{10 - 7}{3 - 0} = \frac{3}{3} = 1.0 \][/tex]
4. For the points [tex]\((11, 13)\)[/tex] and [tex]\((8, 18)\)[/tex]:
[tex]\[ m_4 = \frac{18 - 13}{8 - 11} = \frac{5}{-3} = -1.666 \][/tex]
We need to see which of these calculated slopes matches the given slope of [tex]\(-\frac{5}{3}\)[/tex], which approximately equals [tex]\(-1.666\)[/tex].
Among the calculated slopes, the slope for the points [tex]\((11, 13)\)[/tex] and [tex]\((8, 18)\)[/tex] matches [tex]\(-\frac{5}{3}\)[/tex]:
[tex]\[ -1.666 \approx -\frac{5}{3} \][/tex]
So, the line with a slope of [tex]\(-\frac{5}{3}\)[/tex] could pass through the points [tex]\((11, 13)\)[/tex] and [tex]\((8, 18)\)[/tex].
Thus, the answer is:
[tex]\[ (11, 13), (8, 18) \][/tex]
