Question

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

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