Math Problem Statement

Write down the equation of another line that is parallel to the line y = 3x - 2.

Solution

The question asks to "write down the equation of another line that is parallel to the line y=3x2y = 3x - 2."

Solution:

For two lines to be parallel, they must have the same slope. The equation of the given line is in slope-intercept form y=mx+cy = mx + c, where mm is the slope and cc is the y-intercept.

In the equation y=3x2y = 3x - 2, the slope mm is 3.

A parallel line will also have a slope of 3, but its y-intercept can be different. The general form of a line parallel to this one would be: y=3x+by = 3x + b Where bb can be any constant. For example, one possible answer could be: y=3x+5y = 3x + 5 or any other value for bb.

Would you like further explanation or have any specific questions?

Here are 5 related questions you can explore:

  1. What is the equation of a line perpendicular to y=3x2y = 3x - 2?
  2. How do you find the slope of a line given two points?
  3. What does the slope of a line represent geometrically?
  4. How do you convert a line equation from standard form to slope-intercept form?
  5. What is the relationship between parallel and perpendicular slopes?

Tip: For parallel lines, always remember that the slopes must be equal, but the intercepts can vary.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations

Formulas

Slope-intercept form y = mx + c

Theorems

Parallel Line Theorem

Suitable Grade Level

Grades 8-10