Write as a Vector Equality y=x-3 , y=1/(7x)+3

Problem

y=x−3,y=1/7*x+3

Solution

1. Identify the standard form of the linear equations as y=m*x+b where m is the slope and b is the y-intercept.

2. Determine the direction vector v for each line using the slope m=Δ(y)/Δ(x) where v=([1],[m])

3. Identify a point P on each line, typically the y-intercept (0,b) to serve as the position vector (r_0)=([0],[b])

4. Construct the vector equation of a line using the form r=(r_0)+t*v where t is a scalar parameter.

5. Apply these steps to the first equation y=x−3 where m=1 and b=−3

6. Apply these steps to the second equation y=1/7*x+3 where m=1/7 and b=3

Final Answer

([x],[y])=([0],[−3])+t*([1],[1]),([x],[y])=([0],[3])+s*([7],[1])

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