My Learning Cart
?
Categories
Account

If two lines are parallel and one line has the equation y = 3x + 2, what is the

₹0.0
Login to Download
  • 📥 Instant PDF Download
  • ♾ Lifetime Access
  • 🛡 Secure & Original Content

What’s inside this PDF?

Question: If two lines are parallel and one line has the equation y = 3x + 2, what is the equation of a line parallel to it that passes through the point (1, 4)?

Options:

  1. y = 3x + 1
  2. y = 3x + 4
  3. y = 3x + 2
  4. y = 3x - 1

Correct Answer: y = 3x + 1

Solution: 

A line parallel to y = 3x + 2 will have the same slope (3). Using point-slope form, y - 4 = 3(x - 1) gives y = 3x + 1.

If two lines are parallel and one line has the equation y = 3x + 2, what is the

Practice Questions

Q1
If two lines are parallel and one line has the equation y = 3x + 2, what is the equation of a line parallel to it that passes through the point (1, 4)?
  1. y = 3x + 1
  2. y = 3x + 4
  3. y = 3x + 2
  4. y = 3x - 1

Questions & Step-by-Step Solutions

If two lines are parallel and one line has the equation y = 3x + 2, what is the equation of a line parallel to it that passes through the point (1, 4)?
  • Step 1: Identify the slope of the given line. The equation is y = 3x + 2, so the slope (m) is 3.
  • Step 2: Understand that parallel lines have the same slope. Therefore, the slope of the new line will also be 3.
  • Step 3: Use the point-slope form of a line's equation, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line.
  • Step 4: Substitute the point (1, 4) into the point-slope form. Here, x1 = 1, y1 = 4, and m = 3.
  • Step 5: Write the equation: y - 4 = 3(x - 1).
  • Step 6: Simplify the equation. Distribute 3: y - 4 = 3x - 3.
  • Step 7: Add 4 to both sides to solve for y: y = 3x + 1.
  • Slope of Parallel Lines – Parallel lines have the same slope, which is crucial for determining the equation of a line parallel to a given line.
  • Point-Slope Form – The point-slope form of a line is used to find the equation of a line when a point and the slope are known.
Soulshift Feedback ×

On a scale of 0–10, how likely are you to recommend The Soulshift Academy?

Not likely Very likely
Home Practice Performance eBooks