Question
Jill converted the equation of the line 15 x minus 14 y = negative 2 into slope-intercept form and found the slope and y-intercept of the line as follows.
15 x minus 14 y = negative 2. 15 x minus 4 y minus 15 x = negative 2 minus 15 x. negative 4 y = negative 2 minus 15 x. StartFraction negative 4 y Over negative 4 EndFraction = StartFraction negative 2 minus 15 x Over negative 4 EndFraction. Y = StartFraction negative 2 Over negative 4 EndFraction minus StartFraction 15 x Over negative 4 EndFraction. y = one-half minus StartFraction 15 Over 4 EndFraction x. y = negative StartFraction 15 Over 4 EndFraction x + one-half. slope = negative StartFraction 15 Over 4 EndFraction. y-intercept = one-half.
What was her mistake?
She mixed up the slope and the y-intercept.
She got the sign of the slope wrong.
She got the sign of the y-intercept wrong.
She found the reciprocals of the slope and the y-intercept.
15 x minus 14 y = negative 2. 15 x minus 4 y minus 15 x = negative 2 minus 15 x. negative 4 y = negative 2 minus 15 x. StartFraction negative 4 y Over negative 4 EndFraction = StartFraction negative 2 minus 15 x Over negative 4 EndFraction. Y = StartFraction negative 2 Over negative 4 EndFraction minus StartFraction 15 x Over negative 4 EndFraction. y = one-half minus StartFraction 15 Over 4 EndFraction x. y = negative StartFraction 15 Over 4 EndFraction x + one-half. slope = negative StartFraction 15 Over 4 EndFraction. y-intercept = one-half.
What was her mistake?
She mixed up the slope and the y-intercept.
She got the sign of the slope wrong.
She got the sign of the y-intercept wrong.
She found the reciprocals of the slope and the y-intercept.
Answers
GPT-4o mini
Jill correctly converted the equation of the line into slope-intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.
Her final equation is:
\[
y = -\frac{15}{4}x + \frac{1}{2}
\]
From this equation:
- The slope \(m\) is \(-\frac{15}{4}\)
- The y-intercept \(b\) is \(\frac{1}{2}\)
According to the descriptions of the options:
1. She mixed up the slope and the y-intercept.
2. She got the sign of the slope wrong.
3. She got the sign of the y-intercept wrong.
4. She found the reciprocals of the slope and the y-intercept.
None of these options directly apply since her slope and y-intercept are correctly identified. The slope is negative, and the y-intercept \(\frac{1}{2}\) is positive.
Thus, based on the analysis:
**Answer**: None of the options accurately describe a mistake. However, if a mistake must be identified, it is not clear from the problem statement, as she seems to have done the conversion and identification correctly.
Her final equation is:
\[
y = -\frac{15}{4}x + \frac{1}{2}
\]
From this equation:
- The slope \(m\) is \(-\frac{15}{4}\)
- The y-intercept \(b\) is \(\frac{1}{2}\)
According to the descriptions of the options:
1. She mixed up the slope and the y-intercept.
2. She got the sign of the slope wrong.
3. She got the sign of the y-intercept wrong.
4. She found the reciprocals of the slope and the y-intercept.
None of these options directly apply since her slope and y-intercept are correctly identified. The slope is negative, and the y-intercept \(\frac{1}{2}\) is positive.
Thus, based on the analysis:
**Answer**: None of the options accurately describe a mistake. However, if a mistake must be identified, it is not clear from the problem statement, as she seems to have done the conversion and identification correctly.