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Basic Math/Equation of a Line Parallel to a Given Line through Given Points

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Expert: Josh - 5/7/2011


Question
Help with solving (4,-4)3x-5y=8

Answer
Tracy,

First, rearrange 3x-5y=8 into the standard form y=mx+b  ....[1]
Step 1: 5y=3x-8
Step 2: y=(3/5)x-(8/5) ....[2]

Comparing [2] with [1], it is clear that the gradient "m"=3/5.
Any line parallel to the given line must have the same gradient.
So, the equation must be something like y=(3/5)x+b, where the unknown "b" is the intercept with the y-axis.

Since x=4,y=-4 lies on this new line, it must satisfy the new equation, y=(3/5)x+b. Substituting these values into the equation, we obtain -4=(3/5)*4+b. To make this true, we require b=-4-(12/5).

Thus, the final equation is y=(3/5)x-(32/5).

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Josh

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When I work through problems, I like to emphasize concepts which I believe are worth noting. I will try to answer questions in the following areas, but not at the advanced level. Algebra. Sequences & Series. Trigonometry. Functions & Graphs. Coordinate Geometry. Quadratic Polynomials. Exponential & Logarithms. Basic Calculus. Probability, Permutation and Combination. Mathematical Induction. Complex numbers. Physics problems.

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I have worked as a teaching assistant in college. My hope is that more people will share knowledge without boundary, give help without seeking recognition or monetary rewards.

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Bachelor degree in Engineering Science

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