Write as a Vector Equality y=5x-1 , y=5x-2

Problem

y=5*x−1,y=5*x−2

Solution

1. Identify the given equations as representing two parallel lines in the Cartesian plane, both having a slope of 5

2. Express the lines in vector form r=a+t*v where a is a position vector of a point on the line and v is the direction vector.

3. Determine the direction vector v from the slope m=5 which corresponds to a change of 1 in x for every 5 in y resulting in v=([1],[5])

4. Find a point on each line to serve as the position vector; for y=5*x−1 the yintercept is (0,−1) and for y=5*x−2 the yintercept is (0,−2)

5. Write the vector equations for both lines using a scalar parameter t

Final Answer

([x],[y])=([0],[−1])+t*([1],[5]),([x],[y])=([0],[−2])+t*([1],[5])

Want more problems? Check here!