Question

What is the slope of the line that passes through the points left parenthesis, 2, comma, 3, right parenthesis(2,3) and left parenthesis, 0, comma, 11, right parenthesis(0,11)? Write your answer in simplest form.

Answer 1

To find the slope of a line that passes through two points \((x_1, y_1)\) and \((x_2, y_2)\), you can use the formula for the slope \(m\):

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

In this case, the points are \((2, 3)\) and \((0, 11)\). Assigning the variables:

- \( (x_1, y_1) = (2, 3) \)
- \( (x_2, y_2) = (0, 11) \)

Now plug in the values into the slope formula:

\[
m = \frac{11 - 3}{0 - 2}
\]

Calculate the numerator and the denominator:

\[
m = \frac{8}{-2}
\]

Simplify the fraction:

\[
m = -4
\]

Thus, the slope of the line is \(\boxed{-4}\).