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What is the slope of a line that passes through the points (-1,1/3) and ( 0, -1/3) in the xy-plane?

Sagot :

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]

  • [tex]\(x_1 = -1\)[/tex]
  • [tex]\(y_1 = \frac{1}{3}\)[/tex]
  • [tex]\(x_2 = 0\)[/tex]
  • [tex]\(y_2 = -\frac{1}{3}\)[/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]

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