What is the slope of the line that passes through the points left parenthesis, 7, comma, minus, 5, right parenthesis(7,−5) and left parenthesis, 16, comma, 7, right parenthesis(16,7)? Write your answer in simplest form.

Answer 1

To find the slope of the line that passes through the points \((7, -5)\) and \((16, 7)\), we can use the slope formula:

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

Here, \((x_1, y_1) = (7, -5)\) and \((x_2, y_2) = (16, 7)\). Substituting these values into the formula:

\[ m = \frac{7 - (-5)}{16 - 7} \]

Calculating the differences in the numerator and denominator:

\[ m = \frac{7 + 5}{16 - 7} = \frac{12}{9} \]

Now, simplify \(\frac{12}{9}\):

\[ m = \frac{4}{3} \]

Thus, the slope of the line is

\[ \boxed{\frac{4}{3}} \]