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Solving a line intercept equation


What is A and B so that the line Ay = Bx + 1 passes through points (1, 3) and (5,13) in the Cartesian plane?

I have been trying to solve it using the slope intercept equation to no avail. This is taken from Dale Hoffman's Contemprary Calculus.


Solution

  • First, I would reorder to get canonical form,

    y = (B/A) * x + (1/A) = m * x + b
    

    Now we find slope (m):

    m = dy / dx = (13 - 3) / (5 - 1) = 2.5
    

    sub in to find b:

    3 = 2.5 * 1 + b
    
    b = 0.5
    

    Now sub back to find the values you want,

    b = 0.5 = 1 / A
    
    A = 2
    
    m = 2.5 = B / 2
    
    B = 5