Question

Determine the intercepts of the line.
2x + 5y = -6

Answer 1

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:

`\begin{cases}2x+5y=-6\\y=0\end{cases}\implies 2x=-6 \implies x=-3`

So, the x intercept is (-3,0)

Similarly, for the y axis, we set x=0:

`\begin{cases}2x+5y=-6\\x=0\end{cases}\implies 5y=-6 \implies y=-(6)/(5)`

So, the y intercept is (0,-6/5)