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

Problem

y=−4*x+3,y=1/4*x−2

Solution

1. Identify the slope and a point for the first line y=−4*x+3 The slope is (m_1)=−4 which can be written as the direction vector (v_1)=([1],[−4]) A point on this line is (0,3) giving the position vector (r_01)=([0],[3])

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

(r_1)=([0],[3])+t*([1],[−4])

3. Identify the slope and a point for the second line y=1/4*x−2 The slope is (m_2)=1/4 which can be written as the direction vector (v_2)=([4],[1]) A point on this line is (0,−2) giving the position vector (r_02)=([0],[−2])

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

(r_2)=([0],[−2])+s*([4],[1])

5. Set the two vector equations equal to each other to represent the vector equality of the system.

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

Final Answer

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

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