What are the y-intercept and slope in 6x + 7y - 42 = 0?
Answer and explanation
Correct answer: y-intercept 6, slope -6/7
The governing concept is the slope-intercept form y = mx + c, where m is the slope and c is the y-intercept. Starting with 6x + 7y - 42 = 0, move the x-term and constant to the other side: 7y = -6x + 42. Divide every term by 7 to obtain y = (-6/7)x + 6. Therefore, the coefficient of x is the slope, -6/7, and the constant term is the y-intercept, 6. Option A is correct. Option B reverses both signs, while C and D incorrectly read coefficients from the original standard form without isolating y.
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What is the correct answer to this question?
y-intercept 6, slope -6/7
Why is this the correct answer?
The governing concept is the slope-intercept form y = mx + c, where m is the slope and c is the y-intercept. Starting with 6x + 7y - 42 = 0, move the x-term and constant to the other side: 7y = -6x + 42. Divide every term by 7 to obtain y = (-6/7)x + 6. Therefore, the coefficient of x is the slope, -6/7, and the constant term is the y-intercept, 6. Option A is correct. Option B reverses both signs, while C and D incorrectly read coefficients from the original standard form without isolating y.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Introduction to Polynomials. Topic: Slope and y-intercept.
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