Question

Slope of the line that is perpendicular to the line whose equation $4x+5y=14$, is

• A. $-\frac{4}{5}$
• B. $\frac{5}{4}$
• C. $\frac{4}{5}$
• D. $-\frac{5}{4}$

Answer 1

Answer: (B)

$\frac{5}{4}$

The given equation of the line $l$ is $4x+5y=14$

$\Rightarrow y=-\frac{4x}{5}+\frac{14}{5}$

Therefore, the slope of $l=m_1=-\frac{4}{5}$

Let the line perpendicular to $l$ have a slope $m_2$, then

$m_1\times m_2=-1$

$\therefore -\frac{4}{5}\times m_2=-1$

$\Rightarrow m_2=\frac{5}{4}$