Math Problem Statement

Write the equation of a line parallel to  and with a y-intercept of 2.

Solution

To write the equation of a line parallel to another, we need the slope of the given line. However, since you haven't provided the original line equation, I'll explain the general approach.

The equation of a line is typically written in slope-intercept form: y=mx+by = mx + b where:

  • mm is the slope of the line, and
  • bb is the y-intercept.

Steps:

  1. Find the slope of the original line: For two lines to be parallel, they must have the same slope. So, we would take the slope mm from the original line's equation.
  2. Use the y-intercept: You've specified that the y-intercept is 2, meaning b=2b = 2.

Thus, if the slope mm is known, the equation of the parallel line would be: y=mx+2y = mx + 2

Please provide the original line equation if you need the specific slope.


Would you like more details or have any other questions?

Related questions:

  1. What is the slope of a line, and how do you find it from an equation?
  2. How do you write the equation of a line given two points?
  3. What is the difference between parallel and perpendicular lines in terms of slopes?
  4. How do you convert a line equation from standard form to slope-intercept form?
  5. How do you find the point of intersection between two lines?

Tip: Parallel lines always have the same slope but different y-intercepts unless they are the same line.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Slope-Intercept Form
Parallel Lines

Formulas

y = mx + b

Theorems

Parallel lines theorem: Parallel lines have equal slopes.

Suitable Grade Level

Grades 8-10