Respuesta :
From the picture, we can note that the y-intecept ocurrs at y= -3. Then, we must compare this number with the y-intercepts of the given options. Since the y-intercept ocurrs at x=0, we have:
First option.
By substituting x=0 in this option, we have
[tex]y=\frac{12-0}{4}=3[/tex]which is different from -3. Then, this option is incorrect.
Second option.
By substituting x=0 in this option, we have
[tex]\begin{gathered} 27+3y=0 \\ \text{which gives} \\ y=-\frac{27}{3}=-9 \end{gathered}[/tex]which is different from -3. Then, this option is incorrect.
Third option.
By substituting x=0 in this option, we have
[tex]\begin{gathered} 6y+0=18 \\ \text{which gives } \\ y=\frac{18}{6}=3 \end{gathered}[/tex]which is different from -3. Then, this option is incorrect.
Fourth option.
By substituting x=0 in this option, we have
[tex]\begin{gathered} y+3=0 \\ \text{which gives } \\ y=-3 \end{gathered}[/tex]which is equal to our first result. Then, this option is the correct one.
Therefore, the answer is the last option (4th option).
