Answer:
The standard form of the equation is:
[tex]2y+x=6[/tex]
Hence, option B is true.
Step-by-step explanation:
Given
We know the point-slope of the line equation is
[tex]y-y_1=m\left(x-x_1\right)[/tex]
where m is the slope of the line and (x₁, y₁) is the point
substituting the values m = -1/2 and the point (-4, 5) in the point-slope form
[tex]y-y_1=m\left(x-x_1\right)[/tex]
[tex]y-5=\frac{-1}{2}\left(x-\left(-4\right)\right)[/tex]
[tex]y-5=\frac{-1}{2}\left(x+4\right)[/tex]
Add 5 to both sides
[tex]y-5+5=-\frac{1}{2}\left(x+4\right)+5[/tex]
[tex]y=-\frac{1}{2}x+3[/tex]
Writing the equation in the standard form form
As we know that the equation in the standard form is
[tex]Ax+By=C[/tex]
where x and y are variables and A, B and C are constants
so
[tex]y=-\frac{1}{2}x+3[/tex]
[tex]y+\frac{1}{2}x=3[/tex]
[tex]2y+x=6[/tex]
Thus, the standard form of the equation is:
[tex]2y+x=6[/tex]
Hence, option B is true.
