Question

What is the slope of a line perpendicular to the line whose equation is x-y=6x. Fully reduce your answer.

Answer 1

Answer  

1/5

Step-by-step explanation:

The slope of a perpendicular line is the negative reciprocal. Since y=-5x(m=-5), the slope is -(-1/5) which is 1/5

Answer 2

Answer:

$\boxed{\boxed{\pink{\bf \leadsto Hence \ the \ Slope \ the \ line \ is \ \dfrac{1}{5} . }}}$

Step-by-step explanation:

A linear equation is given to us and we need to find the slope of the line perpendicular to it . Given linear equation to us is ,

$\bf\implies x - y = 6x$

Let's convert this into Slope intercept form to find the slope of the line . The slope intercept form is y = mx + c , where m is the slope of the line.

$\bf\implies x - y = 6x \\\\\bf\implies x - y -6x = 0 \\\\\bf\implies- y - 5x = 0 \\\\\bf\implies y = -5x \\\\\bf\implies \boxed{\red{\bf y = -5x + 0 }}$

Hencs on comparing to the standard form of Slope intercept form of the line , we get to know that the slope of the line is -5.

The equation of a perpendicular line to y = -5x

must have a slope that is the negative reciprocal of the original slope. Hence ,

$\bf\implies m_{perpendicular}= - \dfrac{1}{m}\\\\\bf\implies m_{perpendicular}= -\dfrac{1}{-5}\\\\\bf\implies \boxed{\red{\bf Slope_{perpendicular}= \dfrac{1}{5} }}$

★ Hence the slope of the line is⅕.