If m > 0 and c = 0 in y = mx + c, what is correct about the line?
Answer and explanation
Correct answer: The line increases and passes through the origin
In y = mx + c, the coefficient m determines the direction of the line and c determines its y-intercept. Since m > 0, increasing x produces an increase in y, so the line is increasing rather than decreasing or horizontal. Since c = 0, the equation becomes y = mx; when x = 0, y = 0, so the line passes through the origin. Therefore option B correctly combines both conclusions. Option A reverses the slope behavior, option C would require m = 0, and option D is false because the y-intercept is zero, not negative.
Frequently asked questions
What is the correct answer to this question?
The line increases and passes through the origin
Why is this the correct answer?
In y = mx + c, the coefficient m determines the direction of the line and c determines its y-intercept. Since m > 0, increasing x produces an increase in y, so the line is increasing rather than decreasing or horizontal. Since c = 0, the equation becomes y = mx; when x = 0, y = 0, so the line passes through the origin. Therefore option B correctly combines both conclusions. Option A reverses the slope behavior, option C would require m = 0, and option D is false because the y-intercept is zero, not negative.
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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