[tex]\text{Let}\\\\k:y=m_1x+b_1,\ l:y=m_2x+b_2\\\\\text{Parallel lines have the same slope. Therefore}\\\\l\ \parallel\ k\iff m_2=m_1\\-----------------------------\\\text{The slope-intercept form:}\\\\y=mx+b\\\\m\ -\ slope;\ b\ -\ y-intercept\\-----------------------------[/tex]
[tex]9.\\\text{We have}\\\\4x-3y+9=0\qquad\text{add 3y to both sides}\\\\4x+9=3y\qquad\text{divide both sides by 3}\\\\\dfrac{4}{3}x+3=y\to m=\dfrac{4}{3}\\\\\text{We have the slope}\ m=\dfrac{4}{3}\ \text{and y-intercept}\ b=-1.\\\\\text{Put to the equation of a line:}\\\\\boxed{y=\dfrac{4}{3}x-1}\to\text{slope-intercept form}\\\\y=\dfrac{4}{3}x-1\qquad\text{multiply both sides by 3}\\\\3y=4x-3\qquad\text{subtract 3y from both sides}\\\\\boxed{4x-3y-3=0}\to\text{general form}\\\\===================================[/tex]
[tex]10.\\\text{We have}\\\\5y+x=10\qquad\text{subtract x from both sides}\\\\5y=-x+10\qquad\text{divide both sides by 5}\\\\y=-\dfrac{1}{5}x+2\to m=-\dfrac{1}{5}\\\\\text{We have the slope}\ m=-\dfrac{1}{5}\ \text{and y-intercept}\ b=7.\\\\\text{Put to the equation of a line:}\\\\\boxed{y=-\dfrac{1}{5}x+7}\to\text{slope-intercept form}\\\\y=-\dfrac{1}{5}x+7\qquad\text{multiply both sides by 5}\\\\5y=-x+35\qquad\text{add x to both sides}\\\\\boxed{x+5y=35}\to\text{standard form}[/tex]
