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

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What’s inside this PDF?

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

Options:

5/√10
5/√13
5/√3
5/√2

Correct Answer: 5/√13

Solution:

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

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

Practice Questions

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

5/√10
5/√13
5/√3
5/√2

Questions & Step-by-Step Solutions

If two parallel lines are represented by the equations y = 3x + 1 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 + 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. Here, b1 = 1 and b2 = -4.
Step 5: Use the formula for the distance d between two parallel lines: d = |b2 - b1| / √(1 + m^2).
Step 6: Calculate the difference between the y-intercepts: |b2 - b1| = |-4 - 1| = |-5| = 5.
Step 7: Calculate m^2: m^2 = 3^2 = 9.
Step 8: Calculate 1 + m^2: 1 + 9 = 10.
Step 9: Calculate the square root: √10.
Step 10: Substitute the values into the distance formula: d = 5 / √10.
Step 11: This is the distance between the two parallel lines.

Distance Between Parallel Lines – Understanding how to calculate the distance between two parallel lines given in slope-intercept form.
Slope-Intercept Form – Recognizing the form y = mx + b, where m is the slope and b is the y-intercept.
Absolute Value and Square Root – Applying absolute value and square root in the context of distance calculation.

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

What’s inside this PDF?

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

Practice Questions

Questions & Step-by-Step Solutions

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