Consider a line with slope m and y-intercept (0,5).Find the slope that yields the maximum distance between the origin and the line.
A)The maximum distance of occurs when the slope m is and the line through (0,5) is horizontal.
B)The maximum distance of 5 occurs when the slope m is 0 and the line through (0,5) is horizontal.
C)The maximum distance of occurs when the slope m is 0 and the line through (0,5) is horizontal.
D)The maximum distance of 6 occurs when the slope m is 0 and the line through (0,6) is horizontal.
E)The maximum distance of occurs when the slope m is and the line through (0,5) is horizontal.

Question

Consider a line with slope m and y-intercept (0,5).Find the slope that yields the maximum distance between the origin and the line. ​
A)The maximum distance of occurs when the slope m is and the line through (0,5) is horizontal. 
B)The maximum distance of 5 occurs when the slope m is 0 and the line through (0,5) is horizontal. 
C)The maximum distance of occurs when the slope m is 0 and the line through (0,5) is horizontal. 
D)The maximum distance of 6 occurs when the slope m is 0 and the line through (0,6) is horizontal. 
E)The maximum distance of occurs when the slope m is and the line through (0,5) is horizontal.

Quizplus · Accepted Answer

The distance between the origin and a point (x,y) on the line is given by the equation d = sqrt(x^2 + y^2). Since the y-intercept is (0,5), the equation of the line is y = mx + 5. To find where the maximum distance occurs, we want to minimize d^2, which simplifies to x^2 + (mx+5)^2. Taking the derivative of this expression with respect to m and setting it equal to zero yields m = -x/y = 0 since the line is horizontal. Substituting m = 0 back into the equation of the line gives y = 5. Therefore, the maximum distance occurs when the slope is 0 and the line is horizontal. The distance between the origin and the point (0,5) is 5, so the answer is B.

Consider a Line with Slope M and Y-Intercept (0,5)