Answer:
[tex]\[m = -\frac{2}{3}\][/tex]
Step-by-step explanation:
To find the slope of a line passing through two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] in the xy-plane, you use the formula for the slope:
[tex]\[m = \frac{y_2 - y_1}{x_2 - x_1}\][/tex]
Given the points [tex]\((-1, \frac{1}{3})\) and \((0, -\frac{1}{3})\):[/tex]
Plug these values into the slope formula:
[tex]\[m = \frac{-\frac{1}{3} - \frac{1}{3}}{0 - (-1)} = \frac{-\frac{1}{3} - \frac{1}{3}}{0 + 1} = \frac{-\frac{2}{3}}{1} = -\frac{2}{3}\][/tex]
Thus, the slope of the line that passes through the points [tex]\((-1, \frac{1}{3})\) and \((0, -\frac{1}{3})\)[/tex] is:
[tex]\[m = -\frac{2}{3}\][/tex]