Question

line ab contains points a(4, 5) and b(9, 7). what is the slope of \\(\overleftrightarrow{ab}\\)?
\\(\bigcirc -\frac{5}{2}\\)
\\(\bigcirc -\frac{2}{5}\\)
\\(\bigcirc \frac{2}{5}\\)
\\(\bigcirc \frac{5}{2}\\)

Explanation:

Step1: Recall the slope formula

The slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \).

Step2: Identify the coordinates

For points \( A(4, 5) \) and \( B(9, 7) \), we have \( x_1 = 4 \), \( y_1 = 5 \), \( x_2 = 9 \), \( y_2 = 7 \).

Step3: Substitute into the formula

Substitute the values into the slope formula: \( m=\frac{7 - 5}{9 - 4} \).

Step4: Simplify the expression

Simplify the numerator and the denominator: \( 7 - 5 = 2 \) and \( 9 - 4 = 5 \), so \( m=\frac{2}{5} \).

Answer:

\(\frac{2}{5}\) (corresponding to the option \(\boldsymbol{\frac{2}{5}}\))