Question

find the slope of the line that passes through (10, 8) and (3, 3). 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 \( m=\frac{y_2 - y_1}{x_2 - x_1} \).
Let \((x_1, y_1)=(10, 8)\) and \((x_2, y_2)=(3, 3)\).

Step2: Substitute the values into the formula

Substitute \( x_1 = 10\), \( y_1 = 8\), \( x_2 = 3\), and \( y_2 = 3\) into the slope formula:
\( m=\frac{3 - 8}{3 - 10} \)

Step3: Simplify the numerator and the denominator

Simplify the numerator: \( 3 - 8=- 5 \)
Simplify the denominator: \( 3 - 10=-7 \)
So, \( m = \frac{-5}{-7} \)

Step4: Simplify the fraction

A negative divided by a negative is a positive, so \( \frac{-5}{-7}=\frac{5}{7} \)

Answer:

\(\frac{5}{7}\)