Determine whether the two given lines are perpendicular.
-$$- 4 x + 5 y = 5$$
A) $- 1 \frac { 1 } { 4 } ; ( 0,1 )$

B) $\frac { 4 } { 5 } ; ( 0,1 )$

C) $1 \frac { 1 } { 4 } ; ( 0 , - 1 )$

D) $- \frac { 4 } { 5 } ; ( 0 , - 1 )$

Question

Determine whether the two given lines are perpendicular.
-$$- 4 x + 5 y = 5$$
A) $- 1 \frac { 1 } { 4 } ; ( 0,1 )$

B) $\frac { 4 } { 5 } ; ( 0,1 )$

C) $1 \frac { 1 } { 4 } ; ( 0 , - 1 )$

D) $- \frac { 4 } { 5 } ; ( 0 , - 1 )$

Quizplus · Accepted Answer

The slope-intercept form of a line is $y = mx + b$, where $m$ is the slope. The given equation $-4x + 5y = 5$ can be rearranged to $5y = 4x + 5$, and then $y = \frac{4}{5}x + 1$, which means the slope of the given line is $\frac{4}{5}$. For two lines to be perpendicular, their slopes must be negative reciprocals of each other. Among the options, only option B has a slope of $\frac{4}{5}$, which matches the slope of the given line, indicating it is not the perpendicular line but rather the same line or a parallel line. The question seems to be asking for the slope that would make a line perpendicular to the given line, but based on the provided options and the explanation, there seems to be a misunderstanding in interpreting the question's intent. The correct approach to find a line perpendicular to the given one would involve finding a slope that is the negative reciprocal of $\frac{4}{5}$, which would be $-\frac{5}{4}$. However, none of the options match this criteria directly, indicating a possible error in the question setup or in the selection of the correct answer based on the question's original intent.

Determine Whether the Two Given Lines Are Perpendicular −4x+5y=5- 4 x + 5 y = 5−4x+5y=5

Determine Whether the Two Given Lines Are Perpendicular $- 4 x + 5 y = 5$