Question

What is the equation of the perpendicular line 2x-4y=7 passing through the points (2,-5/4)?

Answer 1

Answer:

$y= 2x-5\frac{1}{4}$

Step-by-step explanation:

We are given;

The equation 2x + 4y = 7

A point (2, -5/4)

We are supposed to determine the equation of a line perpendicular to the given line;

First, we determine the slope of the given line by writing the equation in the form of y= mx + c

2x + 4y = 7

y = -1/2x + 7/4

m₁ = -1/2

But, for perpendicular; m₁×m₂= -1

Therefore;

-1/2 × m₂ = -1

m₂ = 2

Thus, we can get the equation of the line;

Taking another point (x, y)

$\frac{y+\frac{5}{4} }{x-2}=2$

$y+\frac{5}{4}= 2(x-2)$

$y+\frac{5}{4}= 2x-4$

$y= 2x-4-\frac{5}{4}$

$y= 2x-5\frac{1}{4}$

Thus, the equation of the line in question is $y= 2x-5\frac{1}{4}$