Respuesta :
The form of the equation that passes through two points is
[tex]y=mx+b[/tex]m is the slope,
b is the y-intercept
The rule of the slope is
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Let (x1, y1) = (-1, -4) and (x2, y2) = (3, -6)
[tex]\begin{gathered} m=\frac{-6-(-4)}{3-(-1)}=\frac{-6+4}{3+1} \\ m=\frac{-2}{4} \\ m=-\frac{1}{2} \end{gathered}[/tex]The equation is
[tex]y=-\frac{1}{2}x+b[/tex]Substitute x by 3 and y by -6 to find b
[tex]\begin{gathered} -6=-\frac{1}{2}(3)+b \\ -6=-\frac{3}{2}+b \end{gathered}[/tex]Add 3/2 to both sides
[tex]\begin{gathered} -6+\frac{3}{2}=-\frac{3}{2}+\frac{3}{2}+b \\ -\frac{9}{2}=b \end{gathered}[/tex]The equation is
[tex]y=-\frac{1}{2}x-\frac{9}{2}[/tex]The standard form of the linear equation is
[tex]Ax+By=C[/tex]A, B, C are integers
Then multiply all terms in the equation by 2
[tex]2y=-x-9[/tex]Add x to both sides
[tex]\begin{gathered} x+2y=-x+x-9 \\ x+2y=-9 \end{gathered}[/tex]The equation in the standard form is x + 2y = -9
