Question

the graph of the line passing through the points (6,7) and (4,2) has a slope of
$-\frac{5}{2}$
$\frac{5}{2}$
$\frac{2}{5}$
$-\frac{1}{2}$

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

Here, \( (x_1, y_1)=(6, 7) \) and \( (x_2, y_2)=(4, 2) \).

Step3: Substitute into the formula

Substitute the values into the slope formula: \( m=\frac{2 - 7}{4 - 6} \).

Step4: Simplify the numerator and denominator

Simplify the numerator: \( 2 - 7=-5 \).
Simplify the denominator: \( 4 - 6=-2 \).
So, \( m = \frac{-5}{-2}=\frac{5}{2} \).

Answer:

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