The intercepts of a line are the points where the line meets the axes.
If you meet the x axis, then your y coordinate is 0:
[tex]\begin{cases}2x+5y=-6\\y=0\end{cases}\implies 2x=-6 \implies x=-3[/tex]
So, the x intercept is (-3,0)
Similarly, for the y axis, we set x=0:
[tex]\begin{cases}2x+5y=-6\\x=0\end{cases}\implies 5y=-6 \implies y=-\dfrac{6}{5}[/tex]
So, the y intercept is (0,-6/5)
