Question

What is the slope of the line that passes through the points left parenthesis, minus, 6, comma, 5, right parenthesis(−6,5) and left parenthesis, minus, 3, comma, 20, right parenthesis(−3,20)? Write your answer in simplest form.

Answer 1

To find the slope of the line that passes through the points \((-6, 5)\) and \((-3, 20)\), you can use the slope formula:

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

Here, \((x_1, y_1) = (-6, 5)\) and \((x_2, y_2) = (-3, 20)\). Plugging in these values gives:

\[
m = \frac{20 - 5}{-3 - (-6)}
\]

Calculating the differences in the numerator and denominator:

\[
m = \frac{15}{-3 + 6}
\]

\[
m = \frac{15}{3}
\]

Now, simplify:

\[
m = 5
\]

Thus, the slope of the line that passes through the points \((-6, 5)\) and \((-3, 20)\) is \(\boxed{5}\).