Question

Need help on 9-10 asap!! 20 points!!

Answer 1

`\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\\-----------------------------`

`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}\\\\(4)/(3)x+3=y\to m=(4)/(3)\\\\\text{We have the slope}\ m=(4)/(3)\ \text{and y-intercept}\ b=-1.\\\\\text{Put to the equation of a line:}\\\\\boxed{y=(4)/(3)x-1}\to\text{slope-intercept form}\\\\y=(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}\\\\===================================`

`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=-(1)/(5)x+2\to m=-(1)/(5)\\\\\text{We have the slope}\ m=-(1)/(5)\ \text{and y-intercept}\ b=7.\\\\\text{Put to the equation of a line:}\\\\\boxed{y=-(1)/(5)x+7}\to\text{slope-intercept form}\\\\y=-(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}`