Question

what is the slope of the line that passes through the points (2, -4) and (5, 2)? write your answer in simplest form.

Explanation:

Step1: Recall slope formula

The slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \).
Here, \( x_1 = 2 \), \( y_1=-4 \), \( x_2 = 5 \), \( y_2 = 2 \).

Step2: Substitute values into formula

Substitute the values into the slope formula: \( m=\frac{2-(-4)}{5 - 2} \).
Simplify the numerator: \( 2-(-4)=2 + 4=6 \).
Simplify the denominator: \( 5 - 2=3 \).

Step3: Simplify the fraction

Now, \( m=\frac{6}{3}=2 \).

Answer:

\( 2 \)