If two parallel lines are represented by the equations y = 3x + 2 and y = 3x - 4

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Question: If two parallel lines are represented by the equations y = 3x + 2 and y = 3x - 4, what is the distance between these two lines?

Options:

6/√10
2/√10
4/√10
8/√10

Correct Answer: 6/√10

Solution:

The distance between two parallel lines of the form y = mx + b1 and y = mx + b2 is given by |b2 - b1| / √(1 + m^2). Here, |(-4) - 2| / √(1 + 3^2) = 6 / √10.

If two parallel lines are represented by the equations y = 3x + 2 and y = 3x - 4

Practice Questions

If two parallel lines are represented by the equations y = 3x + 2 and y = 3x - 4, what is the distance between these two lines?

6/√10
2/√10
4/√10
8/√10

Questions & Step-by-Step Solutions

If two parallel lines are represented by the equations y = 3x + 2 and y = 3x - 4, what is the distance between these two lines?

Step 1: Identify the equations of the two parallel lines. They are y = 3x + 2 and y = 3x - 4.
Step 2: Recognize that the lines are in the form y = mx + b, where m is the slope and b is the y-intercept.
Step 3: Note that both lines have the same slope (m = 3), which confirms they are parallel.
Step 4: Identify the y-intercepts (b1 and b2) from the equations. Here, b1 = 2 and b2 = -4.
Step 5: Calculate the absolute difference between the y-intercepts: |b2 - b1| = |-4 - 2| = |-6| = 6.
Step 6: Calculate the value of √(1 + m^2). Since m = 3, we find √(1 + 3^2) = √(1 + 9) = √10.
Step 7: Use the formula for the distance between the two parallel lines: Distance = |b2 - b1| / √(1 + m^2). Substitute the values: Distance = 6 / √10.
Step 8: The final answer is the distance between the two lines, which is 6 / √10.

Distance Between Parallel Lines – The formula for calculating the distance between two parallel lines given in slope-intercept form (y = mx + b).
Understanding Slope-Intercept Form – Recognizing the structure of the equations of lines in the form y = mx + b, where m is the slope and b is the y-intercept.

If two parallel lines are represented by the equations y = 3x + 2 and y = 3x - 4

What’s inside this PDF?

If two parallel lines are represented by the equations y = 3x + 2 and y = 3x - 4

Practice Questions

Questions & Step-by-Step Solutions

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