Answer : The correct option is, (A) -8x + 9y = 23
Step-by-step explanation :
The general form for the formation of a linear equation is:
.............(1)
where,
x and y are the coordinates of x-axis and y-axis respectively.
m is slope of line.
First we have to calculate the slope of line.
Formula used :
![m=\frac{(y_2-y_1)}{(x_2-x_1)}](/tpl/images/0179/6573/86f24.png)
Here,
and ![(x_2,y_2)=(\frac{1}{2},3)](/tpl/images/0179/6573/f3e28.png)
![m=\frac{(3-(-1))}{(\frac{1}{2}-(-4))}](/tpl/images/0179/6573/5de20.png)
![m=\frac{8}{9}](/tpl/images/0179/6573/a9fbf.png)
Now put the value of slope in equation 1, we get the linear equation.
![(y-y_1)=m\times (x-x_1)](/tpl/images/0179/6573/59646.png)
![(y-(-1))=\frac{8}{9}\times (x-(-4))](/tpl/images/0179/6573/7c0a3.png)
![(y+1)=\frac{8}{9}\times (x+4)](/tpl/images/0179/6573/0831b.png)
![9\times (y+1)=8\times (x+4)](/tpl/images/0179/6573/733dd.png)
![9y+9=8x+32](/tpl/images/0179/6573/95af5.png)
![9y=8x+32-9](/tpl/images/0179/6573/9a5a0.png)
![9y=8x+23](/tpl/images/0179/6573/483f8.png)
![9y-8x=23](/tpl/images/0179/6573/9ef3c.png)
From the given options we conclude that the option A is an equation of the given line in standard form.
Hence, the correct option is, (A) -8x + 9y = 23