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 $- \frac { 1 } { 5 }$ occurs when the slope m is $- \frac { 1 } { 5 }$ 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 $\frac { 1 } { 5 }$ 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 $- 5$ occurs when the slope m is $\frac { 1 } { 5 }$ 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 $- \frac { 1 } { 5 }$ occurs when the slope m is $- \frac { 1 } { 5 }$ 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 $\frac { 1 } { 5 }$ 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 $- 5$ occurs when the slope m is $\frac { 1 } { 5 }$ and the line through (0,5) is horizontal.

Quizplus · Accepted Answer

The maximum distance between the origin and a line occurs when the line is perpendicular to the line connecting the origin to the line's y-intercept. Since the y-intercept is (0,5), a horizontal line (slope = 0) through this point is already at the maximum distance from the origin, which is 5 units.

Consider a Line with Slope M and Y-Intercept (0,5) −15- \frac { 1 } { 5 }−51​

Consider a Line with Slope M and Y-Intercept (0,5) $- \frac { 1 } { 5 }$