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Write An Equation Of The Line Containing The Given Point And The Parallel To The Given Line. Express Your Answer In The Form Of Y=mx+b (-2,4);4x=5y+7?

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The definition of a parallel line is one that has the same slope.

In the equation Y = mx+b, m is the slope, and thus must remain constant to find a parallel line. So the first step is to find the slope of the line of the equation given. Do this by solving for Y.

4x = 5y + 7,    5y = 4x - 7,    y = (4/5)x - 7/5

From this equation, we can see that the slope of the line is 4/5. This means the equation for the parallel line will have the form:   y = (4/5)x + b

All that's left is to solve for b, using the point given.

4 = (4/5)*-2 + b

b = 4 + 2*4/5 = 4 + 8/5 = 5 3/5

Sub this into our equation and you get the final answer:

Y = (4/5)x + 5 3/5

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