Which line cuts the (y)-axis at ( (0,-8) ) and increases (y) by (18) when (x) increases by (3)?
Answer and explanation
Correct answer: \(y=6x-8\)
The slope is \(\frac{\Delta y}{\Delta x}=\frac{18}{3}=6\). The point \((0,-8)\) shows that the \(y\)-intercept is \(-8\). Therefore, using slope-intercept form \(y=mx+c\), the line is \(y=6x-8\). In \(y=18x-8\), the intercept is correct, but the slope is 18, not 6. Exam tip: find the slope from the changes first, then use the point with \(x=0\) to identify the \(y\)-intercept.
Frequently asked questions
What is the correct answer to this question?
\(y=6x-8\)
Why is this the correct answer?
The slope is \(\frac{\Delta y}{\Delta x}=\frac{18}{3}=6\). The point \((0,-8)\) shows that the \(y\)-intercept is \(-8\). Therefore, using slope-intercept form \(y=mx+c\), the line is \(y=6x-8\). In \(y=18x-8\), the intercept is correct, but the slope is 18, not 6. Exam tip: find the slope from the changes first, then use the point with \(x=0\) to identify 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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