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Find an equation of the line that (a) has y-intercept of 1 and (b) is parallel to the line -3 x -2 y = -9. Write your answer in the form y=mx+b.

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2 Answers

The equation will be in slope-intercept form:     y = mx + b  ,

   where m is the slope of the line and b is the y-intercept.

We are given that the line in question has a y-intercept of 1, which means that  b = 1.

We are also told that the line in question has to be parallel to the line  -3x - 2y = -9. Since parallel lines have the same slope, we need to find the slope of this line by rearranging it into slope-intercept form (y=mx+b). The slope of the line in question will be the same as the slope of this line. 

     -3x - 2y = -9          add 3x to both sides of the equation

     -2y = 3x - 9           divide both sides of the equation by -2

       y = (3x - 9)/-2

         = 3x/(-2)  -  9/(-2)

       y = (-3/2)x + (9/2) 

The equation of the line indicates that the line has a slope of -3/2; that is,  m = -3/2.

We can now determine the equation of the line in question:

     y = mx + b     ,        m = -3/2     and     b = 1

     y = (-3/2)x + 1

Before being able to answer this question, you must understand the properties of a parallel line. In order to find a parallel line, the second line MUST have the same slope as the equation you're given. Before you can see the slope of the equation, you must put the equation into the form of y=mx+b. This yields y=(-3/2)x+(9/2). Thus, the slope of the new line must be -3/2. Knowing this, and that the y-intercept must be 1, you can use the equation y-y1=m(x-x1). y1 is the y-intercept, so plug in 1 for y1 and your slope is -3/2, so plug that in for m. Nothing was specified for x1 so you can just enter 0. Thus, your equation now looks like y-1=(-3/2)(x-0). Solve this equation so that it is in the form of y=mx+b. Your final answer will be y=(-3/2)x+1.