Write as a Vector Equality y=4x+3 , y=4x-4

Problem

y=4*x+3,y=4*x−4

Solution

1. Identify the slope and the direction vector. Both lines have a slope of m=4 which means for every 1 unit increase in x y increases by 4 units. The direction vector v for both lines is ([1],[4])

2. Determine a point on the first line. For y=4*x+3 if x=0 then y=3 A position vector for this line is (r_1)=([0],[3])

3. Determine a point on the second line. For y=4*x−4 if x=0 then y=−4 A position vector for this line is (r_2)=([0],[−4])

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

Final Answer

([x],[y])=([0],[3])+t*([1],[4]),([x],[y])=([0],[−4])+s*([1],[4])

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