Question

What are the intercepts of `3x+9y=-12`?

Answer 1

x-intercept: `(-4)`
y-intercept: `(-4/3)`

Explanation:

Th x-intercept is the point where a graph of the line crosses the X-axis; since all points on the X-axis (and only those points) `y=0`,
another way of saying this is that the x-intercept is the value of `x` when `y=0`
`color(white)("XXX")color(red)(3x+9xx0=-12) rarr color(blue)(3x=-12) rarr color(green)(x=-4)`

Similarly the y-intercept is the value of `y` when `x=0`
`color(white)("XXX")color(red)(3xx0+9y=-12)rarrcolor(blue)(9y=-12)rarrcolor(green)(y=-4/3)`