Line k is defined by y = 17/7x + 4. Line j is parallel to line k in the xy-plane....

1. TRANSLATE the problem information

• Given information:
  • Line k: \(\mathrm{y = \frac{17}{7}x + 4}\)
  • Line j is parallel to line k
• Need to find: slope of line j

2. TRANSLATE the equation format

• The equation \(\mathrm{y = \frac{17}{7}x + 4}\) is in slope-intercept form: \(\mathrm{y = mx + b}\)
• In this form: \(\mathrm{m = slope}\), \(\mathrm{b = y-intercept}\)
• Therefore: slope of line k = \(\mathrm{\frac{17}{7}}\), y-intercept = \(\mathrm{4}\)

3. INFER the relationship between parallel lines

• Parallel lines have identical slopes
• Since line j is parallel to line k, they must have the same slope
• Slope of line j = slope of line k = \(\mathrm{\frac{17}{7}}\)

Answer: B. \(\mathrm{\frac{17}{7}}\)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students confuse the slope with the y-intercept in the equation \(\mathrm{y = \frac{17}{7}x + 4}\).

They see the number 4 at the end and think this represents the slope, forgetting that in \(\mathrm{y = mx + b}\) form, the coefficient of x is the slope. This may lead them to select Choice C (\(\mathrm{4}\)).

Second Most Common Error:

Poor TRANSLATE reasoning: Students incorrectly flip the fraction \(\mathrm{\frac{17}{7}}\) to get \(\mathrm{\frac{7}{17}}\).

This typically happens when students misremember slope formulas or get confused about which number should be in the numerator versus denominator. This may lead them to select Choice A (\(\mathrm{\frac{7}{17}}\)).

The Bottom Line:

This problem tests whether students can correctly identify slope from standard form equations and remember that parallel lines share the same slope - two fundamental concepts that require careful attention to mathematical notation.