Consider a line with slope m and y-intercept (0,8).Write the distance d between the point (7,1) and the line as a function of m.
A) $\frac { 7 | m - 1 | } { \sqrt { m ^ { 2 } + 1 } }$
B) $\frac { 7 | m + 1 | } { \sqrt { m ^ { 2 } - 1 } }$
C) $\frac { 7 | m + 1 | } { \sqrt { m ^ { 2 } + 1 } }$
D) $\frac { 7 | m + 7 | } { \sqrt { m ^ { 2 } + 1 } }$
E) $\frac { | m + 1 | } { \sqrt { m ^ { 2 } + 1 } }$

Question

Consider a line with slope m and y-intercept (0,8).Write the distance d between the point (7,1) and the line as a function of m. 
A) $\frac { 7 | m - 1 | } { \sqrt { m ^ { 2 } + 1 } }$
B) $\frac { 7 | m + 1 | } { \sqrt { m ^ { 2 } - 1 } }$
C) $\frac { 7 | m + 1 | } { \sqrt { m ^ { 2 } + 1 } }$
D) $\frac { 7 | m + 7 | } { \sqrt { m ^ { 2 } + 1 } }$
E) $\frac { | m + 1 | } { \sqrt { m ^ { 2 } + 1 } }$

Quizplus · Accepted Answer

The distance between a point and a line is given by the formula:$$d = \frac{|Ax + By + C|}{\sqrt{A^2 + B^2}}$$where A, B, and C are the coefficients of the line equation. In this case, the line equation is y = mx + 8, so A = m, B = 1, and C = -8. Plugging these values into the formula, we get:$$d = \frac{|m(7) + 1(1) - 8|}{\sqrt{m^2 + 1^2}}$$Simplifying, we get:$$d = \frac{|7m - 7|}{\sqrt{m^2 + 1}}$$$$d = \frac{7|m - 1|}{\sqrt{m^2 + 1}}$$

Consider a Line with Slope M and Y-Intercept (0,8) 7∣m−1∣m2+1\frac { 7 | m - 1 | } { \sqrt { m ^ { 2 } + 1 } }m2+1​7∣m−1∣​

Consider a Line with Slope M and Y-Intercept (0,8) $\frac { 7 | m - 1 | } { \sqrt { m ^ { 2 } + 1 } }$