Answer: [tex]y=-\dfrac67x-\dfrac{34}{7}[/tex]
Step-by-step explanation:
Slope-intercept form: y=mx+c (i) , of linear equations, m= slope and c= y-intercept of the line.
6x+7y=13in slope intercept form would be :
[tex]7y=13-6x\\\\\Rightarrow\ y=\dfrac{-6}{7}x+\dfrac{13}{7}[/tex]
Comparing to (i) , [tex]m = \dfrac{-6}{7}[/tex]
Slope of parallel lines are equal.
So, slope of required line = [tex]m = \dfrac{-6}{7}[/tex]
Equation of line with slope m and passes through point : [tex](y-b)=m(x-a)[/tex]
So, equation of required line:
[tex](y-(-4))=\dfrac{-6}{7}(x-(-1))\\\\\Rightarrow\ (y+4)=\dfrac{-6}{7}(x+1)\\\\\Rightarrow\ y+4=\dfrac{-6}{7}x-\dfrac{6}{7}\\\\\Rightarrow\ y=-\dfrac67x-\dfrac{6}{7}-4\\\\\Rightarrow\ y=-\dfrac67x-\dfrac{34}{7}[/tex]
