Find an equation of the line that passes through the point (2, 4) and is perpendicular to the line 4x + 9y - 2 = 0 (let x be the independent variable and y be the dependent variable.

y = 9/4x -1/2

Step-by-step explanation:

4x + 9y -2=0

solve for y: 4x-2=-9y

(4x-2)/-9 =  

y =4/-9x-2/9

perpendicular means reciprocal of slope. So 4/-9 changesz to 9/4

For the point plug in y and x:

9/4*2+b=4

b = -0.5

I attached graph as proof

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below: