What is the equation of the line perpendicular to x + 3y = 9 and passing through the point (3,0)
3 Answers
justaguide | College Teacher | (Level 2) Distinguished Educator
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
tonys538 | Student, Undergraduate | (Level 1) Valedictorian
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
termpaperexpert | (Level 1) eNoter
y2-y1/x2-x1 =m slope
Passing through the point
3,0
substituting'
x + 3y = 9