https://file.aiquickdraw.com/mathbot/file/1726667006429xhwglvyw.jpg

calculate the distance between each pair of parallel lines. Round answer to one decimal place.

To find the distance between the given pair of parallel lines \( y = 3x + 6 \) and \( y = 3x - 14 \), we use the formula for the distance between two parallel lines of the form \( y = mx + c_1 \) and \( y = mx + c_2 \):

\[
d = \frac{|c_2 - c_1|}{\sqrt{1 + m^2}}
\]

Here, \( m = 3 \), \( c_1 = 6 \), and \( c_2 = -14 \). Let's plug these values into the formula:

\[
d = \frac{|-14 - 6|}{\sqrt{1 + 3^2}}
\]

\[
d = \frac{|-20|}{\sqrt{1 + 9}}
\]

\[
d = \frac{20}{\sqrt{10}}
\]

Now, simplify \( \frac{20}{\sqrt{10}} \):

\[
d = \frac{20}{\sqrt{10}} \times \frac{\sqrt{10}}{\sqrt{10}} = \frac{20\sqrt{10}}{10} = 2\sqrt{10}
\]

To get the final answer, approximate \( 2\sqrt{10} \):

\[
d \approx 2 \times 3.162 = 6.3
\]

So, the distance between the two parallel lines is approximately **6.3** units.

Would you like further details or have any questions?

### Related Questions:
1. How do you find the distance between two lines that are not parallel?
2. What is the slope of each line, and why does it matter when calculating the distance?
3. Can this formula be used if the lines are not in the slope-intercept form?
4. How can this concept be applied in coordinate geometry problems?
5. How do the coefficients in the equation of a line affect its graph?

### Tip:
When calculating the distance between two parallel lines, always ensure they have the same slope \( m \). If not, the lines aren't parallel, and this formula won't apply.

Calculate the distance between each pair of parallel lines y = 3x + 6 and y = 3x - 14. Round the answer to one decimal place.

Learn how to calculate the distance between two parallel lines y = 3x + 6 and y = 3x - 14 using the formula for distance between parallel lines. This step-by-step guide walks through solving the problem, including the necessary algebraic concepts and formulas. Suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation