The equation of required line is [tex]y=-\frac{3}{4} x-\frac{9}{4}[/tex]
Slope-intercept equation :
Equation of line which is given,
[tex]-3x-4y=9\\\\y=\frac{-3x+9}{4} =-\frac{3}{4}x+\frac{9}{4}[/tex]
Compare above equation with [tex]y=mx+c[/tex]
Where m is slope of line, [tex]m=-\frac{3}{4}[/tex]
The slope of parallel lines are always equal.
So that, slope of required line is also [tex]-\frac{3}{4}[/tex].
[tex]y=-\frac{3}{4} x+c[/tex]
the line that passes through the point [tex]P(1,-3)[/tex]
Substitute given point in required equation of line.
[tex]-3=-\frac{3}{4} *1+c\\\\c=-3+\frac{3}{4} \\\\c=-\frac{9}{4}[/tex]
The equation of required line is [tex]y=-\frac{3}{4} x-\frac{9}{4}[/tex]
Learn more about the slope-intercept form of line here:
https://brainly.com/question/1884491
