The line (y=2x+b) passes through ( (1,5) ) and ( (3,9) ). What is (b)?
Answer and explanation
Correct answer: \(3\)
Substitute the point \((1,5)\) into \(y=2x+b\): \(5=2(1)+b\). Hence, \(b=5-2=3\). To verify, when \(x=3\), \(y=2(3)+3=9\), so the second point \((3,9)\) is also satisfied. Here, \(2\) is the slope, whereas \(b\) is the y-intercept. Exam tip: Substitute the coordinates of a given point into the line equation to find an unknown constant.
Frequently asked questions
What is the correct answer to this question?
\(3\)
Why is this the correct answer?
Substitute the point \((1,5)\) into \(y=2x+b\): \(5=2(1)+b\). Hence, \(b=5-2=3\). To verify, when \(x=3\), \(y=2(3)+3=9\), so the second point \((3,9)\) is also satisfied. Here, \(2\) is the slope, whereas \(b\) is the y-intercept. Exam tip: Substitute the coordinates of a given point into the line equation to find an unknown constant.
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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