Suggested languages for you:

Americas

Europe

Problem 219

# Show that the slope of the segment joining $$(1,2)$$ and $$(2,6)$$ is equal to the slope of the segment joining $$(5,15)$$ and $$(10,35)$$

Expert verified
The slopes of the segments joining $$(1,2)$$ and $$(2,6)$$ and $$(5,15)$$ and $$(10,35)$$ are equal, as we calculated both slopes to be 4 using the slope formula $$slope = \frac{y_2-y_1}{x_2-x_1}$$.
See the step by step solution

## Step 1: Find the slope of the segment joining $$(1,2)$$ and $$(2,6)$$

Using the slope formula, we substitute the values from the given coordinates: $$slope_1 = \frac{6-2}{2-1}$$ Now, perform the subtraction in the numerator and denominator: $$slope_1 = \frac{4}{1}$$ So, the slope of this segment is: $$slope_1 = 4$$

## Step 2: Find the slope of the segment joining $$(5,15)$$ and $$(10,35)$$

Now, we will calculate the slope of the second segment using the given coordinates and the slope formula: $$slope_2 = \frac{35-15}{10-5}$$ Subtract the coordinates in the numerator and denominator: $$slope_2 = \frac{20}{5}$$ So, the slope of this segment is: $$slope_2 = 4$$

## Step 3: Compare the two slopes

Now that we have the slopes of both segments, we can compare them to determine if they are equal: $$slope_1 = slope_2$$ Since both slopes are equal to 4, the statement is true. The slopes of the segments joining $$(1,2)$$ and $$(2,6)$$ and $$(5,15)$$ and $$(10,35)$$ are equal.

We value your feedback to improve our textbook solutions.

## Access millions of textbook solutions in one place

• Access over 3 million high quality textbook solutions
• Access our popular flashcard, quiz, mock-exam and notes features

## Join over 22 million students in learning with our Vaia App

The first learning app that truly has everything you need to ace your exams in one place.

• Flashcards & Quizzes
• AI Study Assistant
• Smart Note-Taking
• Mock-Exams
• Study Planner