<em>Ok, so you are given an equation in standard form, 5x+4y=2, and a point, (7, 5). You are being asked to write the equation for a line that is parallel to the equation in standard from, and that includes the point (7, 5). </em>
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<em>First, let's start by finding the slope of your new line. We know that it needs to have the same slope as 5x+4y=2, because parallel lines have the same slopes. To do that, we need to put the equation into slope-intercept form (y=mx+b), which means we need to isolate the "y." </em>
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<em> 5x+4y=2
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<em>-5x -5x (subtract 5x from both sides to move it to the right side of your equation)
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<em>4y = 2 - 5x
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<em>/4 /4 /4 (divide all the terms by 4 to get "y" by itself)
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<em>y = (1/2) - (5/4)x ... I suggest leaving your slope as a fraction.
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<em>Now, we know that our slope, m , is going to be -(5/4). </em>
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<em>Next, we are going to use our slope, -(5/4), and point, (7, 5), to find the b-value (y-intercept) of your new line. Let's plug in what we know:
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<em>y = 5
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<em>m = -(5/4)
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<em>x = 7
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<em>y=mx+b
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<em>5=(-5/4)(7) + b -> I plugged in what we knew for y, m, and x. </em>
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<em>5 = -(35/4) + b -> I multiplied the numbers in the numerator (5 x 7) to get 35/4
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<em>20/4 = -(35/4) + b -> I converted 5 into a faction with a denominator of 4 by multiplying by (4/4)
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<em>+(35/4) +(35/4) -> I add (35/4) to both sides to isolate b
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<em>55/4 = b ... or b = 13.74
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<em>Answer: </em>
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<em>m = -(5/4)
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<em>b = 13.75</em>
