Answer : The correct option is, (C) [tex]y=-\frac{x}{2}[/tex]
Step-by-step explanation :
The general form for the formation of a linear equation is:
[tex](y-y_1)=m\times (x-x_1)[/tex] .............(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 :
[tex]m=\frac{(y_2-y_1)}{(x_2-x_1)}[/tex]
Here,
[tex](x_1,y_1)=(-8,4)[/tex] and [tex](x_2,y_2)=(-6,3)[/tex]
[tex]m=\frac{(3-4)}{(-6-(-8))}[/tex]
[tex]m=\frac{-1}{2}[/tex]
Now put the value of slope in equation 1, we get the linear equation.
[tex](y-y_1)=m\times (x-x_1)[/tex]
[tex](y-4)=\frac{-1}{2}\times (x-(-8))[/tex]
[tex](y-4)=\frac{-1}{2}\times (x+8)[/tex]
[tex]y-4=-\frac{x}{2}-\frac{8}{2}[/tex]
[tex]y-4=-\frac{x}{2}-4[/tex]
[tex]y=-\frac{x}{2}-4+4[/tex]
[tex]y=-\frac{x}{2}[/tex]
From the given options we conclude that the option C is an equation of the given line in standard form.
Hence, the correct option is, (C) [tex]y=-\frac{x}{2}[/tex]
