Find the equation of a line described as follows, and express your answer in point-slope form, slopeintercept form, and standard form.
Find the equation of the line parallel to the line $3x-2y=9$
that passes through the point $(1,-2)$

Step 1 ：The slope of a line given by the equation $ax+by=c$ is $-a/b$. So, the slope of the line $3x-2y=9$ is $-3/2$. A line parallel to this line will have the same slope. So, the slope of the line we are looking for is also $-3/2$.

Step 2 ：The point-slope form of a line is $y-y_1=m(x-x_1)$, where $(x_1,y_1)$ is a point on the line and $m$ is the slope of the line. We can substitute the given point $(1,-2)$ and the slope $-3/2$ into this equation to find the equation of the line in point-slope form.

Step 3 ：The slope-intercept form of a line is $y=mx+b$, where $m$ is the slope of the line and $b$ is the y-intercept. We can rearrange the point-slope form of the line to find the slope-intercept form.

Step 4 ：The standard form of a line is $Ax+By=C$, where $A$, $B$, and $C$ are integers, and $A$ and $B$ are not both zero. We can rearrange the slope-intercept form of the line to find the standard form.

Step 5 ：Final Answer: The equation of the line in point-slope form is $\boxed{{\displaystyle y+2=-\frac{3}{2}(x-1)}}$, in slope-intercept form is $\boxed{{\displaystyle y=-\frac{3}{2}x-1}}$, and in standard form is $\boxed{{\displaystyle 3x+2y=-1}}$.