Welcome to Westonci.ca, the place where your questions are answered by a community of knowledgeable contributors. Get quick and reliable answers to your questions from a dedicated community of professionals on our platform. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.
Sagot :
Answer:
- [tex]\boxed{\sf Standard-form :x + 4y -17=0 }\\[/tex]
- [tex]\boxed{\sf Slope-intercept\ form :y =\dfrac{-1}{4}x +\dfrac{17}{4}}[/tex]
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]
We hope our answers were helpful. Return anytime for more information and answers to any other questions you may have. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.