Question

find the slope of the line that passes through (10, 10) and (5, 3). simplify your answer and write it as a proper fraction, improper fraction, or integer.

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, \((x_1, y_1)=(10, 10)\) and \((x_2, y_2)=(5, 3)\).

Step2: Substitute values into formula

Substitute \( x_1 = 10\), \( y_1 = 10\), \( x_2 = 5\), \( y_2 = 3\) into the formula:
\( m=\frac{3 - 10}{5 - 10} \)

Step3: Simplify numerator and denominator

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

Step4: Simplify the fraction

The negatives cancel out, so \( m = \frac{7}{5} \)

Answer:

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