Write as a Vector Equality y=-1/2x+4 , y=-1/2x-2

Problem

y=−1/2*x+4,y=−1/2*x−2

Solution

1. Identify the slope and the y-intercept for each line to determine the direction and position vectors.

2. Determine the direction vector v from the slope m=−1/2 which corresponds to a change of 2 in x for every −1 in y

v=([2],[−1])

3. Select a point on each line to serve as the position vector (r_0) For the first line, the y-intercept is (0,4) For the second line, the y-intercept is (0,−2)

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

5. Express the lines as a set of vector equalities.

Final Answer

([x],[y])=([0],[4])+t*([2],[−1]),([x],[y])=([0],[−2])+s*([2],[−1])

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