Write an equation of the line containing the given point and perpendicular to the given line:
(4, - 7); 9x+5y=3

Step-by-step explanation:

Given equation of line:

To find the equation of line perpendicular to the line of the given equation and passes through point (4,-7).

Writing the given equation of line in standard form.

Subtracting both sides by

Dividing both sides by 5.

Rearranging the equation in standard form

Applying slope relationship between perpendicular lines.

where and are slopes of perpendicular lines.

For the given equation in the form the slope can be found by comparing with standard form.

∴

Thus slope of line perpendicular to this line would be given as:

∴

The line passes through point (4,-7)

Using point slope form:

Where and

So,

Using distribution.

Subtracting 7 to both sides.

Taking LCD to subtract fractions

Thus, the equation of line in standard form is given by: