Write as a Vector Equality y=3/4x-3 , y=-2/5x+1

Problem

y=3/4*x−3,y=−2/5*x+1

Solution

1. Identify the standard vector form for a line in ℝ2 which is r=(r_0)+t*v where (r_0) is a position vector to a point on the line and v is the direction vector.

2. Determine the components for the first line y=3/4*x−3 A point on the line is (0,−3) The slope m=3/4 implies that for every 4 units of horizontal change, there are 3 units of vertical change, giving a direction vector <4,3>

3. Write the vector equation for the first line.

([x],[y])=([0],[−3])+t*([4],[3])

4. Determine the components for the second line y=−2/5*x+1 A point on the line is (0,1) The slope m=−2/5 implies a direction vector of <5,−2>

5. Write the vector equation for the second line using a different scalar parameter s()

([x],[y])=([0],[1])+s*([5],[−2])

Final Answer

(r_1)=([0],[−3])+t*([4],[3]),(r_2)=([0],[1])+s*([5],[−2])

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