Question is in description.

Question

Find the equation for the line that passes through the point (1, 1), and that is perpendicular to the line with the equation −3/4x − y = −4.

Answer 1

The given line is described by the equation: 

−3/4x − y = −4 

=> -y=3/4x - 4 

=>y= -3/4x +4 ... is the standard form and gives that this line has a slope=-3/4

therefore any line perpendicular to it must have a slope = 4/3

If such a line passes through (1,1) its equation will be:

y-1=4/3(x-1)

=>3y-3=4x-4

=>4x-3y=1 ... is the desired equation.

Answer 2

Shatoria, we need to use the equation

 

y - y₁= m(x - x₁)

 

x₁ and y₁ come from our point, and m is the slope. Remember that perpendicular lines have opposite reciprocal slopes.

 

-3/4x - y = -4

           -y = 3/4x - 4

            y = -3/4x + 4

 

So, m in our equation is 4/3.

 

y - 1 = 4/3(x - 1)

y - 1 = 4/3x - 4/3

     y = 4/3x - 1/3

 

Hope this helps!

 

Answer 3

Hi Shatoria,

 

Given the equation

-3/4 x - y = -4

 

We first need to find the slope of this line.

-3/4 x + 4 = y

Giving us a slope of -3/4

 

For two lines to be perpendicular then the slope of the 2nd line must be the negative inverse of the slope of the 1st line.

Since the slope of the given line is -3/4, then the slope of the line we need to find will be +4/3

 

Now recall the point slope form of the equation of a line.

 

y-y₁ = m(x-x₁)  where m = slope and (x₁,y₁) is the point given (1,1).

 

y-1 = 4/3 (x-1)

y-1 = 4/3 x - 4/3

y = 4/3 x - 4/3 + 1

y = 4/3 x - 1/3  This is the slope intercept form

 

We can also use the standard form

y = 4/3 x - 1/3

3y = 4x -1

4x - 3y = 1