the general equation of the line is
[tex]y=mx+b[/tex]where m is the slope and b the y-intercept represented as (0,b)
from the graph we can know the y-mtercept because is the point where the line touches the y-axis
so, is (0,-6) then b=-6
replace b
[tex]y=mx-6[/tex]ow to calculate the slope we can take a point from the line and replace
i will use (4,10)
so replacing
[tex]\begin{gathered} (10)=m(4)-6 \\ \end{gathered}[/tex]and solve for m
[tex]\begin{gathered} 10+6=4m \\ 4m=16 \\ m=\frac{16}{4} \\ \\ m=4 \end{gathered}[/tex]the slope is 4
Finally, repalce b and m to find the equation of the line
[tex]y=4x-6[/tex]so the right option is fourth
