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 from the origin to the line $y = mx + 2$ is given by the formula $d = \frac{|c|}{\sqrt{1 + m^2}}$, where $c$ is the y-intercept. Here, $c = 2$, so $d = \frac{2}{\sqrt{1 + m^2}}$.

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) $d = \frac { m } { \sqrt { m ^ { 2 } + 2 } }$