W.2 Find the slope from two points

Question

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Find the slope of the line that passes through (2, 1) and (10, 6).

Simplify your answer and write it as a proper fraction, improper fraction, or integer.

Answer 1

To find the slope \( m \) of the line that passes through two points \((x_1, y_1)\) and \((x_2, y_2)\), you can use the formula:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

For the points given \((2, 1)\) and \((10, 6)\):

• Let \((x_1, y_1) = (2, 1)\)
• Let \((x_2, y_2) = (10, 6)\)

Now plug the values into the formula:

\[ m = \frac{6 - 1}{10 - 2} = \frac{5}{8} \]

The slope of the line that passes through the points \((2, 1)\) and \((10, 6)\) is

\[ \frac{5}{8} \]