Answer:
Step-by-step explanation:
Here a equation of the line is given to us and we need to find out the equation of line which passes through the given point and parallel to the given line , the given equation is ,
[tex]\longrightarrow x + 4y = 7\\[/tex]
Firstly convert it into slope intercept form of the line which is y = mx + x , as ;
[tex]\longrightarrow 4y = -x + 7 \\[/tex]
[tex]\longrightarrow y =\dfrac{-x}{4}+\dfrac{7}{4}\\[/tex]
On comparing it to y = mx + c , we have ,
[tex]\longrightarrow m =\dfrac{-1}{4}\\[/tex]
[tex]\longrightarrow c =\dfrac{7}{4}\\[/tex]
Now as we know that the slope of two parallel lines is same . Therefore the slope of the parallel line will be ,
[tex]\longrightarrow m_{||)}=\dfrac{-1}{4}\\[/tex]
Now we may use point slope form of the line as ,
[tex]\longrightarrow y - y_1 = m(x-x_1) \\[/tex]
On substituting the respective values ,
[tex]\longrightarrow y - 5 =\dfrac{-1}{4}\{ x -(-3)\}\\[/tex]
[tex]\longrightarrow y -5=\dfrac{-1}{4}(x+3)\\[/tex]
[tex]\longrightarrow 4(y -5 ) =-1(x +3) \\[/tex]
[tex]\longrightarrow 4y -20 = - x -3 \\[/tex]
[tex]\longrightarrow x + 4y -20+3=0\\[/tex]
[tex]\longrightarrow \underset{Standard \ Form }{\underbrace{\underline{\underline{ x + 4y -17=0}}}} \\[/tex]
Again the equation can be rewritten as ,
[tex]\longrightarrow y - 5 = \dfrac{-1}{4}(x +3) \\[/tex]
[tex]\longrightarrow y = \dfrac{-1}{4}x -\dfrac{3}{4}+5 \\[/tex]
[tex]\longrightarrow y = \dfrac{-1}{4}x -\dfrac{20-3}{4} \\[/tex]
[tex]\longrightarrow \underset{Slope-Intercept\ form }{\underbrace{\underline{\underline{ y =\dfrac{-1}{4}x +\dfrac{17}{4}}}}}\\[/tex]
