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.

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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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**

_{1}=m(x-x_{1}). y_{1} is the y-intercept, so plug in 1 for y_{1} and your slope is -3/2, so plug that in for m. Nothing was specified for x_{1} 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.