If (y=ax-7) and (y=6x+5) have equal slopes, what is (y) on the first line at (x=3)?
Answer and explanation
Correct answer: 11
In the form \(y=mx+c\), the coefficient of \(x\) is the slope. Since the slopes are equal, \(a=6\). Substituting \(x=3\) in the first line gives \(y=6\times3-7=11\). The \(5\) is the y-intercept of the second line, so it does not affect the y-value of the first line. Exam tip: first equate the slopes to find the unknown coefficient, then substitute the given value of \(x\).
Frequently asked questions
What is the correct answer to this question?
11
Why is this the correct answer?
In the form \(y=mx+c\), the coefficient of \(x\) is the slope. Since the slopes are equal, \(a=6\). Substituting \(x=3\) in the first line gives \(y=6\times3-7=11\). The \(5\) is the y-intercept of the second line, so it does not affect the y-value of the first line. Exam tip: first equate the slopes to find the unknown coefficient, then substitute the given value of \(x\).
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Introduction to Polynomials. Topic: Slope and y-intercept.
