Math Problem Statement

Which of the following lines is parallel to: y = 2/5 x - 9?

Solution

To determine which line is parallel to y=25x9y = \frac{2}{5}x - 9, we need to identify lines with the same slope. Parallel lines share identical slopes but can have different y-intercepts.

The given line y=25x9y = \frac{2}{5}x - 9 has a slope of 25\frac{2}{5}.

Now, let’s check the slopes of each option:

  1. y=7x+9y = 7x + 9 — Slope = 7
  2. y=25x+11y = \frac{2}{5}x + 11 — Slope = 25\frac{2}{5}
  3. y=52x+4y = \frac{5}{2}x + 4 — Slope = 52\frac{5}{2}
  4. y=52x3y = -\frac{5}{2}x - 3 — Slope = 52-\frac{5}{2}

Only option 2, y=25x+11y = \frac{2}{5}x + 11, has the same slope (25\frac{2}{5}) as the given line. Therefore, it is the correct answer.

Would you like a more detailed explanation or have any questions?

Here are 5 related questions for further understanding:

  1. What is the difference between parallel and perpendicular lines in terms of slopes?
  2. How do you determine if two lines are perpendicular?
  3. Can two lines with different y-intercepts be parallel?
  4. How can you identify the slope and y-intercept in an equation in slope-intercept form?
  5. Why does the y-intercept not affect whether two lines are parallel?

Tip: Remember, in slope-intercept form y=mx+by = mx + b, the slope mm determines the line's angle, while the intercept bb only shifts its position vertically.

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Math Problem Analysis

Mathematical Concepts

Algebra
Slope-Intercept Form
Parallel Lines

Formulas

Slope-intercept form y = mx + b

Theorems

Parallel lines have equal slopes

Suitable Grade Level

Grades 7-9