Math Problem Statement

What is the slope of a line parallel to y = 9x + 2?

Solution

To determine the slope of a line parallel to the given line, we first examine the equation provided:

y=9x+2y = 9x + 2

In the equation y=mx+by = mx + b, mm represents the slope. Here, m=9m = 9, so the slope of this line is 9.

Since parallel lines have the same slope, a line parallel to y=9x+2y = 9x + 2 will also have a slope of 9.

Would you like further details on this concept, or do you have any questions?

Here are some related questions to consider:

  1. What would be the slope of a line perpendicular to y=9x+2y = 9x + 2?
  2. How can you find the slope if the equation is given in a different form, like 2xy=32x - y = 3?
  3. What effect does changing the bb value (the y-intercept) have on parallel lines?
  4. How do you find the equation of a line parallel to y=9x+2y = 9x + 2 that passes through a specific point?
  5. Can two lines with different slopes ever be parallel?

Tip: Remember, for two lines to be parallel, they must have the same slope but can have different y-intercepts.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Slopes of Parallel Lines

Formulas

Slope-intercept form y = mx + b

Theorems

Parallel Lines Theorem

Suitable Grade Level

Grades 8-10