[tex]\boxed{y+1=\frac{3}{2}(x-4)}[/tex]
Explanation:
We can write the equation of the given line in Slope-Intercept form:
[tex]3x-2y=9 \\ \\ \\ Isolating \ y: \\ \\ 3x-9=2y \\ \\ y=\frac{3}{2}x-\frac{9}{2} \\ \\ \\ Where: \\ \\ Slope: \ m=\frac{3}{2} \\ \\ y-intercept: \ b=-\frac{9}{2}[/tex]
The line we are looking for is parallel to our given line, that is, they have the same slope. So, writing the Point-Slope form of our unknown line we have:
[tex]y-y_{0}=m(x-x_{0}) \\ \\ m=\frac{3}{2} \\ \\ (x_{0},y_{0})=(4,-1) \\ \\ \\ Substituting \ values: \\ \\ y-(-1)=\frac{3}{2}(x-4) \\ \\ \\ \boxed{y+1=\frac{3}{2}(x-4)}[/tex]
Learn more:
Point slope form: https://brainly.com/question/13771268#
#LearnWithBrainly
