Graphs, functions, and coordinates

AI Thread Summary
To solve the problem of finding λ and μ for the line ε: y=(-λ+μ)x +2λ -μ, which passes through point A(0,1) and is parallel to line ζ: y=-2x + 2008, it is established that the slope of line ε must equal -2, the slope of line ζ. This leads to the equation -λ + μ = -2. Additionally, substituting x=0 into the equation for line ε gives the equation 2λ - μ = 1. The system of equations formed by these two relationships can be solved to find the values of λ and μ. Understanding that parallel lines share the same slope is crucial for this problem.
PhysicS FAN
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Homework Statement


If a staight ε: y=(-λ+μ)x +2λ -μ , (where μ and λ are real numbers) passes through point A(0,1) and is parallel to an other straight lin. ζ: y= -2x + 2008 find λ and μ

Homework Equations

The Attempt at a Solution


It is clear that when x=0 we know that 2λ-μ=1 which is one of the equations we should use to solve the system. Also the second line is of type y= -αx+ β and since they are parallel the same and for the first line What upsests me is the parallel lines which I don't know how to work with. PLease help me.
 
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PhysicS FAN said:

Homework Statement


If a staight ε: y=(-λ+μ)x +2λ -μ , (where μ and λ are real numbers) passes through point A(0,1) and is parallel to an other straight lin. ζ: y= -2x + 2008 find λ and μ

Homework Equations

The Attempt at a Solution


It is clear that when x=0 we know that 2λ-μ=1 which is one of the equations we should use to solve the system. Also the second line is of type y= -αx+ β and since they are parallel the same and for the first line What upsests me is the parallel lines which I don't know how to work with. PLease help me.
Parallel lines have the same slope. The slope of the second line is -2. What must be the slope of the first line?

Why not call the lines L1 and L2? Greek letters are almost never used as labels for lines.
 
Mark44 said:
Parallel lines have the same slope. The slope of the second line is -2. What must be the slope of the first line?

Why not call the lines L1 and L2? Greek letters are almost never used as labels for lines.
Thank you for your help. (It's a Greek book the one that I saw the problem:smile:)
 

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