Answer:
[tex]y= 2x-5\frac{1}{4}[/tex]
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)
[tex]\frac{y+\frac{5}{4} }{x-2}=2[/tex]
[tex]y+\frac{5}{4}= 2(x-2)[/tex]
[tex]y+\frac{5}{4}= 2x-4[/tex]
[tex]y= 2x-4-\frac{5}{4}[/tex]
[tex]y= 2x-5\frac{1}{4}[/tex]
Thus, the equation of the line in question is [tex]y= 2x-5\frac{1}{4}[/tex]
