Answer:
[tex]y=-7x-11[/tex]
Step-by-step explanation:
Given:
The two points on the line are [tex](-2,3)[/tex] and [tex](-1,-4)[/tex].
The slope of the line joining two points [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] is given as:
[tex]Slope,m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Here, [tex]x_{1}=-2,y_{1}=3,x_{2}=-1,y_{2}=-4[/tex]
∴ [tex]m=\frac{-3-4}{-1-(-2)}=\frac{-7}{-1+2}=\frac{-7}{1}=-7[/tex]
Equation of line with a point [tex](x_{1},y_{1})[/tex] and slope [tex]m[/tex] is given as:
[tex]y-y_{1}=m(x-x_{1})[/tex]
Plug in -2 for [tex]x_{1}[/tex], 3 for [tex]y_{1}[/tex] and -7 for [tex]m[/tex]. This gives,
[tex]y-3=-7(x-(-2))\\y-3=-7(x+2)\\y-3=-7x-(7\times 2)\\y-3=-7x-14\\y=-7x-14+3\\y=-7x-11[/tex]
Therefore, the equation of the line in vertex form is [tex]y=-7x-11[/tex].
