Question

Find the equation of the straight line passing through the point 0,2 which is perpendicular to the line 1/4x + 5

Answer 1

Answer:

slope of our line is - 4

and y intercept is 2 ( from 0,2)

our line is :

y =-4x +2

Answer 2

To find:

The equation of the straight line passing through the point (0, 2) and perpendicular to the line $y=\dfrac{1}{4}x+5$

Step-by-step explanation:

• If $m$ be the slope of the required perpendicular line, then
• $\quad m\times\dfrac{1}{4}=-1$
• $\Rightarrow m=-4$

• We can consider the equation of the required perpendicular line to be
• $\quad y=-4x+c$ ... ... (i)

• Since (i) passes through the point (0, 2), then
• $\quad 2=-4\times 0+c$
• $\Rightarrow c=2$

• Putting $c=2$ in (i), we get the required straight line as
• $\quad y=-4x+2$
• $\Rightarrow 4x+y=2$

Final Answer:

The equation of the required perpendicular straight line is $4x+y=2$.