a line whose perpendicular distance from the origin is 4 units and the slope of perpendicular is 2÷3. Find the equation of the line.

Step-by-step explanation:

The equation of a line:

We have

substitute:

The formula of a distance between a point and a line:

General form of a line:

Point:

Distance:

Convert the equation:

    |subtract from both sides

   |multiply both sides by 3

Coordinates of the point:

substitute:

   |multiply both sides by

  |divide both  sides by 3

Finally:

the required function is .

step-by-step explanation:

from the given table it is noticed that the graph passing through (-3,7), (0,4), (3,1) and (8,-4).

it is a linear function because the value of y is decrease by one as the value of x increase by 1.

the slope of the function is

the slope of the function is -1 and the y-intercept is 4.

the slope intercept form is

where, m is slope and b is y-intercept.

therefore the required function is . the graph of this function is shown below.