If two parallel lines are represented by the equations y = 3x + 1 and y = 3x - 4

₹0.0

Question: If two parallel lines are represented by the equations y = 3x + 1 and y = 3x - 4, what is the distance between them?

Options:

Correct Answer: 4/√10

Solution:

The distance between two parallel lines y = mx + b1 and y = mx + b2 is |b2 - b1| / √(1 + m^2). Here, |(-4) - 1| / √(1 + 3^2) = 5 / √10 = 5/√10.

If two parallel lines are represented by the equations y = 3x + 1 and y = 3x - 4, what is the distance between them?

If two parallel lines are represented by the equations y = 3x + 1 and y = 3x - 4, what is the distance between them?

Step 1: Identify the equations of the two parallel lines. They are y = 3x + 1 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. For the first line, b1 = 1, and for the second line, b2 = -4.
Step 5: Use the formula for the distance between two parallel lines: Distance = |b2 - b1| / √(1 + m^2).
Step 6: Calculate |b2 - b1|: |(-4) - 1| = |-5| = 5.
Step 7: Calculate m^2: m^2 = 3^2 = 9, so 1 + m^2 = 1 + 9 = 10.
Step 8: Calculate the square root: √(10).
Step 9: Substitute the values into the distance formula: Distance = 5 / √(10).
Step 10: The final answer for the distance between the two parallel lines is 5 / √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.