# What is the equation of the line perpendicular to x + 3y = 9 and passing through the point (3,0)

*print*Print*list*Cite

### 3 Answers

The equation of the line x + 3y = 9 can be written in the slope intercept form y = mx + c as `y = -x/3 + 3` . The slope of this line is `-1/3` . As the product of the slope of perpendicular lines is equal to -1, the slope of a line perpendicular to x + 3y = 9 is 3.

If the perpendicular line passes through the point (3,0) its equation is `(y - 0)/(x - 3) = 3`

=> y = 3x - 9

**The equation of the line perpendicular to x + 3y = 9 and passing through the point (3,0) is y = 3x - 9**

The equation of a line in slope-intercept form is y = mx + c where m is the slope.

For the line with equation x + 3y = 9, rewriting the equation gives:

3y = 9 - x

y = 3 - x/3

The slope of this line is -1/3. The product of the slope of a line perpendicular to this line with the slope of the line is equal to -1. It follows that a line perpendicular to x + 3y = 9 has slope 3.

If the line passes through the point (3,0) its equation is (y - 0)/(x - 3) = 3

y = 3x - 9

The required equation of the line is y = 3x - 9

y2-y1/x2-x1 =m slope

Passing through the point

3,0

substituting'

**x + 3y = 9 **