Question

Write an equation (a) in slope-intercept form and (b) in standard form for the line passing through (-3,5) and parallel to x + 4y=7

Answer 1

Answer:

• $\boxed{\sf Standard-form :x + 4y -17=0 }$

• $\boxed{\sf Slope-intercept\ form :y =\dfrac{-1}{4}x +\dfrac{17}{4}}$

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 ,

$\longrightarrow x + 4y = 7$

Firstly convert it into slope intercept form of the line which is y = mx + x , as ;

$\longrightarrow 4y = -x + 7$

$\longrightarrow y =\dfrac{-x}{4}+\dfrac{7}{4}$

On comparing it to y = mx + c , we have ,

$\longrightarrow m =\dfrac{-1}{4}$

$\longrightarrow c =\dfrac{7}{4}$

Now as we know that the slope of two parallel lines is same . Therefore the slope of the parallel line will be ,

$\longrightarrow m_{||)}=\dfrac{-1}{4}$

Now we may use point slope form of the line as ,

$\longrightarrow y - y_1 = m(x-x_1)$

On substituting the respective values ,

$\longrightarrow y - 5 =\dfrac{-1}{4}\{ x -(-3)\}$

$\longrightarrow y -5=\dfrac{-1}{4}(x+3)$

$\longrightarrow 4(y -5 ) =-1(x +3)$

$\longrightarrow 4y -20 = - x -3$

$\longrightarrow x + 4y -20+3=0$

$\longrightarrow \underset{Standard \ Form }{\underbrace{\underline{\underline{ x + 4y -17=0}}}}$

Again the equation can be rewritten as ,

$\longrightarrow y - 5 = \dfrac{-1}{4}(x +3)$

$\longrightarrow y = \dfrac{-1}{4}x -\dfrac{3}{4}+5$

$\longrightarrow y = \dfrac{-1}{4}x -\dfrac{20-3}{4}$

$\longrightarrow \underset{Slope-Intercept\ form }{\underbrace{\underline{\underline{ y =\dfrac{-1}{4}x +\dfrac{17}{4}}}}}$