Let line t be the line represented by 3x+4y = 5 and let line p be the line perpendicular to line t and containing the point (5,5) . What is the x-coordinate of the point common to line t and line p ? Express your answer as a common fraction.

tertre
Apr 18, 2017

#1
**+2 **

3x + 4y = 5 the slope of this line = -3/4.....so....the slope of a perpendicular line will be 4/3

And the equation of a line with this slope passing through (5,5) is

y = (4/3) (x - 5) + 5

y = (4/3)x - 20/3 + 5

y = (4/3)x - 5/3

Subbing this into 3x + 4y = 5 for y , we have

3x + 4[ (4/3)x - 5/3] = 5

3x + (16/3 )x - 20/3 = 5 simplify

(25/3)x = 35/3

25x = 35 divide both sides by 25

x = 35/25 = 7/5 and this is the x coordinate of the intersection of line t and p

CPhill
Apr 18, 2017