Question

1. what is the slope of the line that passes through the points (5, 4) and (5, -5)? write your answer in simplest form.
2. what is the slope of the line that passes through the points (9, -1) and (21, 1)? write your answer in simplest form.

Explanation:

Problem 11

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, \((x_1,y_1)=(5,4)\) and \((x_2,y_2)=(5, - 5)\).

Step2: Substitute values into formula

Substitute \( x_1 = 5,y_1 = 4,x_2 = 5,y_2=-5 \) into the formula: \( m=\frac{-5 - 4}{5 - 5}=\frac{-9}{0} \). Division by zero is undefined, so the slope is undefined.

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, \((x_1,y_1)=(9,-1)\) and \((x_2,y_2)=(21,1)\).

Step2: Substitute values into formula

Substitute \( x_1 = 9,y_1=-1,x_2 = 21,y_2 = 1 \) into the formula: \( m=\frac{1-(-1)}{21 - 9}=\frac{1 + 1}{12}=\frac{2}{12} \).

Step3: Simplify the fraction

Simplify \(\frac{2}{12}\) by dividing numerator and denominator by their greatest common divisor, which is 2. So \(\frac{2\div2}{12\div2}=\frac{1}{6}\).

Answer:

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Problem 12