Determine whether the two given lines are perpendicular.
-$$5 x + 7 y = 48$$
A) $- \frac { 5 } { 7 } ; \left( 0 , \frac { 48 } { 7 } \right)$

B) $1 \frac { 2 } { 5 } ; \left( 0 , \frac { 7 } { 48 } \right)$

C) $- 1 \frac { 2 } { 5 } ; \left( 0 , \frac { 7 } { 48 } \right)$

D) $\frac { 5 } { 7 } ; \left( 0 , \frac { 48 } { 7 } \right)$

Question

Determine whether the two given lines are perpendicular.
-$$5 x + 7 y = 48$$
A) $- \frac { 5 } { 7 } ; \left( 0 , \frac { 48 } { 7 } \right)$

B) $1 \frac { 2 } { 5 } ; \left( 0 , \frac { 7 } { 48 } \right)$

C) $- 1 \frac { 2 } { 5 } ; \left( 0 , \frac { 7 } { 48 } \right)$

D) $\frac { 5 } { 7 } ; \left( 0 , \frac { 48 } { 7 } \right)$

Quizplus · Accepted Answer

Two lines are perpendicular if and only if their slopes (coefficients of $x$ and $y$ when in slope-intercept form) are negative reciprocals of each other. The given line can be rearranged to slope-intercept form as $y = -\frac{5}{7}x + \frac{48}{7}$, so its slope is $-\frac{5}{7}$. The line perpendicular to it will have a slope that is the negative reciprocal of $-\frac{5}{7}$, which is $\frac{7}{5}$.

Using the point-slope formula with the given point $\left(0,\frac{48}{7}ight)$, the equation of the perpendicular line is $y - \frac{48}{7} = \frac{7}{5}(x - 0)$, which simplifies to $y = \frac{7}{5}x + \frac{48}{7}$. Comparing this to the given equation, we see that the slopes are negative reciprocals of each other, so the answer is $\boxed{	ext{(A)}}$.

Determine Whether the Two Given Lines Are Perpendicular 5x+7y=485 x + 7 y = 485x+7y=48

Determine Whether the Two Given Lines Are Perpendicular $5 x + 7 y = 48$