Write as a Vector Equality y=-2x+8 , y=-2x-4 , 6x+3y=6

Problem

y=−2*x+8,y=−2*x−4,6*x+3*y=6

Solution

1. Identify the standard form of the lines. The first two equations are already in slope-intercept form y=m*x+b The third equation 6*x+3*y=6 can be simplified by dividing by 3 to get 2*x+y=2 which is y=−2*x+2

2. Observe that all three lines have the same slope m=−2 This means the lines are parallel and can be represented by a single vector equation with a varying parameter for the constant term.

3. Express the general form of the lines as 2*x+y=d where d is a constant. In vector notation, this is the dot product of a normal vector and a position vector.

4. Define the normal vector n using the coefficients of x and y Here, n=([2],[1])

5. Write the vector equality by setting the dot product of the normal vector and the position vector r=([x],[y]) equal to the set of constants D={8,−4,2}

Final Answer

([2],[1])⋅([x],[y])={8,−4,2}

Want more problems? Check here!