Answer : The correct option is, (A) -8x + 9y = 23
Step-by-step explanation :
The general form for the formation of a linear equation is:
\((y-y_1)=m\times (x-x_1)\) .............(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 :
\(m=\frac{(y_2-y_1)}{(x_2-x_1)}\)
Here,
\((x_1,y_1)=(-4,-1)\) and \((x_2,y_2)=(\frac{1}{2},3)\)
\(m=\frac{(3-(-1))}{(\frac{1}{2}-(-4))}\)
\(m=\frac{8}{9}\)
Now put the value of slope in equation 1, we get the linear equation.
\((y-y_1)=m\times (x-x_1)\)
\((y-(-1))=\frac{8}{9}\times (x-(-4))\)
\((y+1)=\frac{8}{9}\times (x+4)\)
\(9\times (y+1)=8\times (x+4)\)
\(9y+9=8x+32\)
\(9y=8x+32-9\)
\(9y=8x+23\)
\(9y-8x=23\)
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
