Write as a Vector Equality y=3x+6 , y=-1/3x+5

Problem

y=3*x+6,y=−1/3*x+5

Solution

1. Identify the slope-intercept form y=m*x+b for each line to determine the direction vectors.

2. Determine the direction vector v for the first line y=3*x+6 Since the slope m=3 the vector is (v_1)=([1],[3])

3. Identify a point on the first line by setting x=0 which gives the position vector (r_0)=([0],[6])

4. Write the vector equation for the first line using the parameter t

([x],[y])=([0],[6])+t*([1],[3])

5. Determine the direction vector v for the second line y=−1/3*x+5 Since the slope m=−1/3 the vector is (v_2)=([3],[−1])

6. Identify a point on the second line by setting x=0 which gives the position vector (r_0)=([0],[5])

7. Write the vector equation for the second line using the parameter s()

([x],[y])=([0],[5])+s*([3],[−1])

Final Answer

([x],[y])=([0],[6])+t*([1],[3]),([x],[y])=([0],[5])+s*([3],[−1])

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