Question

find the slope of the line that passes through (7, 11) and (10, 4). simplify your answer and write it as a proper fraction, improper fraction, or integer.

Explanation:

Step1: Recall the slope formula

The slope \( m \) of a line passing through 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, \( (x_1, y_1)=(7, 11) \) and \( (x_2, y_2)=(10, 4) \).

Step2: Substitute the values into the formula

Substitute \( x_1 = 7,y_1 = 11,x_2 = 10,y_2 = 4 \) into the slope formula: \( m=\frac{4 - 11}{10 - 7} \).

Step3: Simplify the numerator and denominator

Calculate the numerator: \( 4-11=-7 \). Calculate the denominator: \( 10 - 7 = 3 \). So \( m=\frac{-7}{3}=-\frac{7}{3} \).

Answer:

\(-\frac{7}{3}\)