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. Both lines have a slope of m=1/2 The first line has a y-intercept of (0,−4) and the second line has a y-intercept of (0,2)

2. Determine the direction vector v from the slope. Since m=rise/run=1/2 the direction vector can be written as v=([2],[1])

3. Express each line in vector form r=(r_0)+t*v where (r_0) is the position vector of the y-intercept and t is a scalar parameter.

4. Write the vector equation for the first line using the point (0,−4)

([x],[y])=([0],[−4])+t*([2],[1])

5. Write the vector equation for the second line using the point (0,2)

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

Final Answer

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

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