<h3>
Answer: 3x-2y = 5 (choice A)</h3>
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Explanation:
The given graph passes through (0,2) and (2,5)
The slope of this line is
m = (y2 - y1)/(x2 - x1)
m = (5-2)/(2-0)
m = 3/2
Since the y intercept is b = 2, we go from y = mx+b to y = (3/2)x+2, which is the equation of the graphed line shown.
Any parallel line will have the same slope, but a different y intercept.
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The parallel line must pass through (x,y) = (3,2). We'll use these coordinates along with m = 3/2 to find the y intercept b
y = mx+b
2 = (3/2)(3)+b
2 = 9/2+b
2-9/2 = b
4/2 - 9/2 = b
-5/2 = b
b = -5/2 ... is the new y intercept
The equation of the parallel line is y = (3/2)x-5/2, which is in slope intercept form
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Let's convert to standard form
y = (3/2)x-5/2
2y = 3x-5 .... multiply everything by the LCD 2 to clear out fractions
2y+5 = 3x
3x = 2y+5
3x-2y = 5 ... is the equation in standard form of the parallel line
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As a check, we can plug (x,y) = (3,2) into that last equation above to get
3x-2y = 5
3*3-2*2 = 5 ... replace x with 3, replace y with 2
9-4 = 5
5 = 5
Confirming that (x,y) = (3,2) is on the line.
