[tex]\begin{gathered} \text{general straight line equation is} \\ y=mx+b \\ x-\text{intercept at (4,0) means that} \\ 0=m(4)+b\Rightarrow4m+b=0 \\ y-\text{intercept at (0,-6) means that} \\ -6=m(0)+b\Rightarrow-6=b \\ \text{hence b=-6} \\ \text{Substituying this values in 4m+b=0, one has} \\ 4m+(-6)=0 \\ 4m-6=0 \\ 4m=6 \\ m=\frac{6}{4} \\ m=\frac{3}{2} \\ \text{then, the equation must be} \\ y=\frac{3}{2}x-6 \end{gathered}[/tex]
