In the line y = -x + 12, what are the slope and y-intercept?
Answer and explanation
Correct answer: Slope -1, y-intercept 12
The governing concept is the slope-intercept form of a straight line, y = mx + c, where m is the slope and c is the y-intercept. Comparing y = -x + 12 with this standard form, the coefficient of x is -1, so m = -1. The constant term is 12, so the line crosses the y-axis at (0, 12), and its y-intercept is 12. Therefore, option B gives both values correctly. Option A reverses the two quantities, option C changes the sign of the slope, and option D incorrectly treats the numbers as reciprocals or rearranged coefficients. The negative slope also means that y decreases by 1 whenever x increases by 1.
Frequently asked questions
What is the correct answer to this question?
Slope -1, y-intercept 12
Why is this the correct answer?
The governing concept is the slope-intercept form of a straight line, y = mx + c, where m is the slope and c is the y-intercept. Comparing y = -x + 12 with this standard form, the coefficient of x is -1, so m = -1. The constant term is 12, so the line crosses the y-axis at (0, 12), and its y-intercept is 12. Therefore, option B gives both values correctly. Option A reverses the two quantities, option C changes the sign of the slope, and option D incorrectly treats the numbers as reciprocals or rearranged coefficients. The negative slope also means that y decreases by 1 whenever x increases by 1.
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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