Question

Write parametric equations of the line with the equation 2x+3y=5

Answer 1

We have
2x+3y=5

Step 1
find two points of the line
for x=0--------------> y=5/3     point (0,1.67)
for y=0 --------------> x=5/2    point (2.5,0)

The vector between two points is v =(2.5-0,0-1.67)=(2.5.-1.67)

Vector form: r=ro+tv----------> (2.5,0)+(2.5,-1.67)t

Parametric form 
x=2.5+2.5t
y=-1.67t

the answer is 
x=2.5+2.5t
y=-1.67t