When (6x+3y=18) is written in (y=mx+c) form, what are the slope and (y)-intercept?
Answer and explanation
Correct answer: Slope (-2), (y)-intercept (6)
The slope-intercept form of a line is \\(y=mx+c\\), where \\(m\\) is the slope and \\(c\\) is the y-intercept. Start with \\(6x+3y=18\\). To isolate \\(y\\), subtract \\(6x\\) from both sides, obtaining \\(3y=-6x+18\\). Dividing every term by 3 gives \\(y=-2x+6\\).
Comparing this result with \\(y=mx+c\\), the coefficient of \\(x\\) is \\(m=-2\\), and the constant term is \\(c=6\\). The line therefore crosses the y-axis at \\(6\\), when \\(x=0\\), and falls by 2 units in \\(y\\) for every unit increase in \\(x\\). Thus option A is correct. A positive slope would ignore the negative sign produced when \\(6x\\) is moved to the other side.
Frequently asked questions
What is the correct answer to this question?
Slope (-2), (y)-intercept (6)
Why is this the correct answer?
The slope-intercept form of a line is \\(y=mx+c\\), where \\(m\\) is the slope and \\(c\\) is the y-intercept. Start with \\(6x+3y=18\\). To isolate \\(y\\), subtract \\(6x\\) from both sides, obtaining \\(3y=-6x+18\\). Dividing every term by 3 gives \\(y=-2x+6\\).
Comparing this result with \\(y=mx+c\\), the coefficient of \\(x\\) is \\(m=-2\\), and the constant term is \\(c=6\\). The line therefore crosses the y-axis at \\(6\\), when \\(x=0\\), and falls by 2 units in \\(y\\) for every unit increase in \\(x\\). Thus option A is correct. A positive slope would ignore the negative sign produced when \\(6x\\) is moved to the other side.
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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