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

Question

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

Answer 1

To find the slope of the line that passes through the points \((10, 1)\) and \((1, 6)\), we can use the slope formula:

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

Here, we can assign:

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

Now, substitute the values into the formula:

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

Calculating the differences:

\[ m = \frac{5}{1 - 10} = \frac{5}{-9} \]

Simplifying the fraction gives:

\[ m = -\frac{5}{9} \]

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

\[ \boxed{-\frac{5}{9}}. \]

Answer 2

Find the slope of the line that passes through (8, 9) and (3, 1).

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

Answer 3

To find the slope of the line that passes through the points \((8, 9)\) and \((3, 1)\), we can use the slope formula:

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

We'll assign:

• \((x_1, y_1) = (8, 9)\)
• \((x_2, y_2) = (3, 1)\)

Now, substitute the values into the formula:

\[ m = \frac{1 - 9}{3 - 8} \]

Calculating the differences yields:

\[ m = \frac{-8}{-5} \]

This simplifies to:

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

Therefore, the slope of the line that passes through the points \((8, 9)\) and \((3, 1)\) is

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