Write as a Vector Equality m=-1/5 , b=1

Problem

m=−1/5,b=1

Solution

1. Identify the slope-intercept form of a linear equation, which is y=m*x+b

2. Substitute the given values m=−1/5 and b=1 into the equation to get y=−1/5*x+1

3. Express the line in vector form r=(r_0)+t*v where (r_0) is a position vector to a point on the line and v is the direction vector.

4. Determine a point on the line by setting x=0 which gives y=1 resulting in the position vector (r_0)=<0,1>

5. Determine the direction vector v using the slope m=Δ(y)/Δ(x)=(−1)/5 which corresponds to the vector <5,−1>

6. Combine these components into the vector equality <x,y>=<0,1>+t<5,−1>

Final Answer

<x,y>=<0,1>+t<5,−1>

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