If (y=6x+(v-11)) and (y=(v+5)x+10) have the same (y)-intercept, what is the slope of the second line?
Answer and explanation
Correct answer: 26
In the form \(y=mx+c\), the \(y\)-intercept is \(c\). The first line has \(y\)-intercept \(v-11\), while the second has \(y\)-intercept \(10\). Since they are equal, \(v-11=10\), so \(v=21\). Therefore, the slope of the second line is \(v+5=21+5=26\). Option \(25\) would result from incorrectly taking \(v=20\). Exam tip: in \(y=mx+c\), \(m\) is the slope and \(c\) is the \(y\)-intercept.
Frequently asked questions
What is the correct answer to this question?
26
Why is this the correct answer?
In the form \(y=mx+c\), the \(y\)-intercept is \(c\). The first line has \(y\)-intercept \(v-11\), while the second has \(y\)-intercept \(10\). Since they are equal, \(v-11=10\), so \(v=21\). Therefore, the slope of the second line is \(v+5=21+5=26\). Option \(25\) would result from incorrectly taking \(v=20\). Exam tip: in \(y=mx+c\), \(m\) is the slope and \(c\) is the \(y\)-intercept.
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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