Question

what is the slope of the line that passes through the points (-2, 9) and (8, 34)? 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 \( m=\frac{y_2 - y_1}{x_2 - x_1} \).
Here, \( x_1=-2 \), \( y_1 = 9 \), \( x_2=8 \), \( y_2 = 34 \).

Step2: Substitute values into formula

Substitute the values: \( m=\frac{34 - 9}{8-(-2)} \).
Simplify numerator and denominator: \( 34 - 9 = 25 \), \( 8-(-2)=8 + 2=10 \).
So \( m=\frac{25}{10} \).

Step3: Simplify the fraction

Simplify \( \frac{25}{10} \) by dividing numerator and denominator by their greatest common divisor, which is 5.
\( \frac{25\div5}{10\div5}=\frac{5}{2} \).

Answer:

\( \frac{5}{2} \)