If (y=3x+(v-5)) and (y=(v+2)x+6) have the same (y)-intercept, what is the slope of the second line?
Answer and explanation
Correct answer: 13
In the form \(y=mx+c\), \(c\) is the \(y\)-intercept. The first line has \(y\)-intercept \(v-5\), while the second has \(y\)-intercept \(6\). Since they are equal, \(v-5=6\), so \(v=11\). The slope of the second line is the coefficient of \(x\), namely \(v+2\); hence it is \(11+2=13\). Option 11 is the value of \(v\), not the slope. Exam tip: in \(y=mx+c\), the coefficient of \(x\) is always the slope.
Frequently asked questions
What is the correct answer to this question?
13
Why is this the correct answer?
In the form \(y=mx+c\), \(c\) is the \(y\)-intercept. The first line has \(y\)-intercept \(v-5\), while the second has \(y\)-intercept \(6\). Since they are equal, \(v-5=6\), so \(v=11\). The slope of the second line is the coefficient of \(x\), namely \(v+2\); hence it is \(11+2=13\). Option 11 is the value of \(v\), not the slope. Exam tip: in \(y=mx+c\), the coefficient of \(x\) is always the slope.
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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