Write as a Vector Equality

Problem

y=2*x−1,y=−3*x+4,y=−x+2,y=−1/3*x+1,y=4/3*x−4

Solution

1. Identify the standard vector form of a line in ℝ2 which is r=(r_0)+t*v where (r_0) is a position vector ((x_0),(y_0)) and v is the direction vector (1,m)

2. Determine the slope m and the y-intercept b for each equation to find a point (0,b) and a direction vector (1,m)

3. Convert y=2*x−1 using point (0,−1) and slope 2

4. Convert y=−3*x+4 using point (0,4) and slope −3

5. Convert y=−x+2 using point (0,2) and slope −1

6. Convert y=−1/3*x+1 using point (0,1) and slope −1/3 To avoid fractions in the direction vector, use (3,−1)

7. Convert y=4/3*x−4 using point (0,−4) and slope 4/3 To avoid fractions in the direction vector, use (3,4)

Final Answer

([x],[y])=([0],[−1])+t*([1],[2])

([x],[y])=([0],[4])+t*([1],[−3])

([x],[y])=([0],[2])+t*([1],[−1])

([x],[y])=([0],[1])+t*([3],[−1])

([x],[y])=([0],[−4])+t*([3],[4])

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