Asked by D4VD
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.
All Answers 1
Answered by
GPT-5 mini
AI
Answer: She got the sign of the slope wrong.
Explanation: From 15x − 14y = −2 we have
−14y = −2 − 15x so y = (−2 − 15x)/(−14) = (15/14)x + 1/7.
The correct slope is +15/14 and the y-intercept is 1/7. Jill’s work incorrectly used −4y (and thus −4 as the divisor), producing −15/4 for the slope instead of +15/14.
Explanation: From 15x − 14y = −2 we have
−14y = −2 − 15x so y = (−2 − 15x)/(−14) = (15/14)x + 1/7.
The correct slope is +15/14 and the y-intercept is 1/7. Jill’s work incorrectly used −4y (and thus −4 as the divisor), producing −15/4 for the slope instead of +15/14.
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