Question

line passes through points (2, 5) and (15, 9). What is its slope?

Answer 1

• Answer:

$\Large{\boxed{\sf Slope = \dfrac{4}{13} }}$

• Explanation:

The slope of a line passing through two points, also known as its gradient, is calculated using the slope formula.

$\Large{\left[ \begin{array}{c c c} \underline{\tt Slope \ formula \text{:}} \\~ \\ \tt m = \dfrac{rise}{run} = \dfrac{\Delta y}{\Delta x} = \dfrac{y_2 - y_1}{x_2 - x_1}\end{array} \right] }$

Where m is the slope of the line.

First, let's identify our values:

$\sf (\underbrace{\sf 2}_{x_1} \ , \ \overbrace{\sf 5}^{y_1} ) \ \ and \ \ (\underbrace{\sf 15}_{x_2} \ , \ \overbrace{\sf 9}^{y_2} )$

Now, substitute these values into the formula:

$\sf \rightarrow m = \dfrac{9 - 5}{15 - 2} \\ \\ \\ \rightarrow \boxed{\boxed{\sf m = \dfrac{4}{13} }}$