Question

What is the slope of the line that passes through the points left parenthesis, minus, 5, comma, 7, right parenthesis(−5,7) and left parenthesis, minus, 2, comma, 4, right parenthesis(−2,4)? Write your answer in simplest form.

Answer 1

To find the slope of the line that passes through the points \((-5, 7)\) and \((-2, 4)\), we can use the slope formula:

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

Here, \((x_1, y_1) = (-5, 7)\) and \((x_2, y_2) = (-2, 4)\).

Now, substituting the coordinates into the formula:

\[
m = \frac{4 - 7}{-2 - (-5)}
\]

Calculating the numerator:

\[
4 - 7 = -3
\]

Calculating the denominator:

\[
-2 - (-5) = -2 + 5 = 3
\]

Now we put the numerator and the denominator together:

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

Simplifying this gives:

\[
m = -1
\]

Thus, the slope of the line that passes through the points \((-5, 7)\) and \((-2, 4)\) is \(\boxed{-1}\).