Answer:
The equation of line is:
[tex]8x-9y=-23[/tex]
Step-by-step explanation:
We are given that a graph is a that passes through two points:
[tex](-4,-1)[/tex] and [tex](\dfrac{1}{2},3)[/tex]
We know that the equation of line passing through two points:
[tex](a,b)[/tex] and [tex](c,d)[/tex] is given by:
[tex]y-b=\dfrac{d-b}{b-a}\times (x-a)[/tex]
Here we have:
[tex](a,b)=(-4,-1)[/tex] and [tex](c,d)=(\dfrac{1}{2},3)[/tex]
Hence, the equation of line is:
[tex]y-(-1)=\dfrac{3-(-1)}{\dfrac{1}{2}-(-4)}\times (x-(-4))\\\\y+1=\dfrac{3+1}{\dfrac{1}{2}+4}\times (x+4)\\\\y+1=\dfrac{4}{\dfrac{9}{2}}\times (x+4)\\\\y+1=\dfrac{4\times 2}{9}\times (x+4)\\\\y+1=\dfrac{8}{9}\times (x+4)\\\\9\times (y+1)=8\times (x+4)\\\\9y+9=8x+8\times 4\\\\9y+9=8x+32\\\\8x-9y=9-32\\\\8x-9y=-23[/tex]
Hence the equation of line is:
[tex]8x-9y=-23[/tex]
