If in (y=(a-4)x+a), the difference between slope and (y)-intercept is (-4), which statement is correct?
Answer and explanation
Correct answer: For every real value of a
In the standard form y=mx+c, m is the slope and c is the y-intercept. Here, the slope is a-4 and the y-intercept is a. Hence, their difference is \((a-4)-a=-4\), which does not depend on the value of a. Therefore, the statement is true for every real value of a. Although a=4 also works, it is not the only value. Exam tip: Identify m and c first, then simplify the stated difference.
Frequently asked questions
What is the correct answer to this question?
For every real value of a
Why is this the correct answer?
In the standard form y=mx+c, m is the slope and c is the y-intercept. Here, the slope is a-4 and the y-intercept is a. Hence, their difference is \((a-4)-a=-4\), which does not depend on the value of a. Therefore, the statement is true for every real value of a. Although a=4 also works, it is not the only value. Exam tip: Identify m and c first, then simplify the stated difference.
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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