Answer:
[tex]6x-7y=11[/tex]
Step-by-step explanation:
we know that
The equation of the line in standard form is equal to
[tex]Ax+By=C[/tex]
step 1
Find the slope m
Let
[tex]A(-3,-1), B(1/2,2)[/tex]
[tex]m=\frac{2+1}{(1/2)+3}\\ \\m=\frac{6}{7}[/tex]
step 2
The equation of the line in point-slope form is equal to
[tex]y-y1=m(x-x1)[/tex]
with the slope m and the point B find the equation of the line
[tex]y+1=\frac{6}{7}(x+3)[/tex] ------> multiply by 7 both sides
[tex]7y+7=6(x+3)[/tex]
[tex]7y+7=6x+18[/tex]
convert to standard form
[tex]6x-7y=18-7[/tex]
[tex]6x-7y=11[/tex]
