# Which equation represents a line parallel to the line whose equation is 􏰃-2x + 3y 􏰂= -􏰃4 ?

Which equation represents a line parallel to the line whose equation is 􏰃-2x + 3y 􏰂= -􏰃4 and passes through the point (1,3)?

(1) y􏰃-3=-􏰂􏰃3/2(x􏰃-1)

(2) y􏰃-3=􏰂􏰂􏰃 2/3(x􏰃- 1)

(3) y+􏰄3=􏰂􏰃 -3/2(x􏰄+1)

(4) y+􏰄3=􏰂2/3(x􏰄+1)

To solve this problem, we must first remember that two parallel lines have equal slopes. To find the slope of the first line, we can put it into the form y=mx+b where m is the slope

-2x + 3y 􏰂= -􏰃4

3y = 2x-4

y=2/3x-4/3

Therefore, the slope of the first line is 2/3

Now that we know the slope we can find the equation of the line by using the following formula

y1-y2=m(x1-x2). Since the problem says that the new line must pass through the point (1,3), we can plug in the x and y values in to the equation.

y1-y2=m(x1-x2)

y-3=2/3 (x-1)

Choice 2 is the correct answer choice.

Note: For a line perpendicular to another line, the slope will be negative reciprocal.

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