Question

Write, in slope-intercept-form, the inequality shown in the graph.

Two points which the boundary line intersects are shown.

Answer 1

`y \leqslant -x + 1`

Explanation:

First write the equation of the line with either inequality sign, like so:

`y \geqslant -x + 1`

Then check to see if the equation is true. The easiest way to do this is to plug the coordinates (0,0) into the equation:

`0 \geqslant -0 + 1 \\ 0 \geqslant 1`

Since 0 > 1 is false, you know that the correct inequality must be:

`y \leqslant -x + 1`

If you want to check this, plug the coordinates (0,0) into the equation:

`0 \leqslant -0 + 1 \\ 0 \leqslant 1`

Since 0 < 1 is true, you know this equation is correct.

I hope that helped! If I made a mistake, just let me know.