The point-slope form:
[tex]y-y_1=m(x-x_1)\\\\m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points [tex](-4,\ -1)[/tex] and [tex]\left(\dfrac{1}{2},\ 3\right)[/tex].
Substitute:
[tex]m=\dfrac{3-(-1)}{\frac{1}{2}-(-4)}=\dfrac{4}{4\frac{1}{2}}=\dfrac{4}{\frac{9}{2}}=4\cdot\dfrac{2}{9}=\dfrac{8}{9}\\\\y-(-1)=\dfrac{8}{9}(x-(-4))\\\\y+1=\dfrac{8}{9}(x+4)[/tex]
The standard form: Ax + By = C
[tex]y+1=\dfrac{8}{9}(x+4)\qquad\text{multiply both sides by 9}\\\\9y+9=8(x+4)\qquad\text{use distributive property}\\\\9y+9=8x+32\qquad\text{subtract 9 from both sides}\\\\9y=8x+23\qquad\text{subtract 8x from both sides}\\\\-8x+9y=23\qquad\text{change the signs}\\\\\boxed{8x-9y=23}[/tex]
