If (y=6x+b) and (y=-4x+8) cut the (y)-axis at the same point, what is (b)?
Answer and explanation
Correct answer: 8
To find a y-intercept, put \(x=0\) in the equation of the line. The y-intercept of the first line is \(b\), while for the second line, putting \(x=0\) gives \(y=8\). Since both lines cut the y-axis at the same point, their y-intercepts must be equal: \(b=8\). The numbers \(6\) and \(-4\) are slopes, not y-intercepts. Exam tip: in \(y=mx+c\), \(c\) is the y-intercept directly.
Frequently asked questions
What is the correct answer to this question?
8
Why is this the correct answer?
To find a y-intercept, put \(x=0\) in the equation of the line. The y-intercept of the first line is \(b\), while for the second line, putting \(x=0\) gives \(y=8\). Since both lines cut the y-axis at the same point, their y-intercepts must be equal: \(b=8\). The numbers \(6\) and \(-4\) are slopes, not y-intercepts. Exam tip: in \(y=mx+c\), \(c\) is the y-intercept directly.
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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