Intercept of Two LinesDate: 06/07/99 at 13:45:20 From: Jeff Burger Subject: Locate intercept of two sloping lines Helping my son with math has started to stretch my abilities a little. I also found that I could use this in my work if I could solve it. We need to locate the intercept point of two lines. If the y = mx + b is given (standard form) for two lines, how do we calculate the exact location without graphing. Basically then y = m1*x + b1 = m2*x + b2 or m1*x + b1 = m2*x + b2 then m1*x = m2*x + b2 - b1 then x = m2*x + b2 - b1 -------------- m1 How do I isolate "x"? Date: 06/07/99 at 17:52:36 From: Doctor Arthur Subject: Re: Locate intercept of two sloping lines Jeff, It looks as if you started off really well, but you forgot to combine like terms. You were correct when you said m1*x = m2*x + b2 - b1, but instead of dividing by m1, subtract m2*x from both sides to get: m1*x - m2*x = b2-b1 If you factor x, you get x(m1-m2) = b2-b1 Then just divide both sides by (m1-m2) and you get x = (b2-b1)/(m1-m2) Remember that b1, b2, m1, and m2 are all real numbers; therefore your answer is either some type of fraction, or an integer. I hope that this answers your question, and that you'll come back with other questions you may have. - Doctor Arthur, The Math Forum http://mathforum.org/dr.math/ |
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