Consider a line with slope m and y-intercept (0,2).Write the distance d between the origin and the line as a function of m.
A) $d = \frac { m } { \sqrt { m ^ { 2 } + 2 } }$
B) $d = \frac { 1 } { \sqrt { m ^ { 2 } - 2 } }$
C) $d = \frac { 1 } { \sqrt { m ^ { 2 } + 2 } }$
D) $d = \frac { 2 } { \sqrt { m ^ { 2 } - 1 } }$
E) $d = \frac { 2 } { \sqrt { m ^ { 2 } + 1 } }$

Question

Consider a line with slope m and y-intercept (0,2).Write the distance d between the origin and the line as a function of m. ​
A) $d = \frac { m } { \sqrt { m ^ { 2 } + 2 } }$
B) $d = \frac { 1 } { \sqrt { m ^ { 2 } - 2 } }$
C) $d = \frac { 1 } { \sqrt { m ^ { 2 } + 2 } }$
D) $d = \frac { 2 } { \sqrt { m ^ { 2 } - 1 } }$
E) $d = \frac { 2 } { \sqrt { m ^ { 2 } + 1 } }$

Quizplus · Accepted Answer

The distance $d$ between the origin and a line with equation $y = mx + b$ (where $b$ is the y-intercept) is given by the formula $d = \frac{|b|}{\sqrt{m^2 + 1}}$. Here, $b = 2$, so $d = \frac{2}{\sqrt{m^2 + 1}}$, which matches choice E.

Consider a Line with Slope M and Y-Intercept (0,2) d=mm2+2d = \frac { m } { \sqrt { m ^ { 2 } + 2 } }d=m2+2​m​

Consider a Line with Slope M and Y-Intercept (0,2) $d = \frac { m } { \sqrt { m ^ { 2 } + 2 } }$