Question

which inequality matches the graph

Answer 1

The question is missing the graph, therefore, I will provide the steps to solve it and you apply those steps to the graph.

It would be great if you can attach the graph though.

1- We first start by getting the equation on the line:

The equation for a linear line is: y = mx + c

where m is the slope and c is the y-intercept

Take any two points on the line and get the slope using the following equation:

$m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

The m in the equation is now known. To get the c, take any point that belong to the line and substitute with this point in the equation. The only unknown would be c which can easily be calculated.

Now, the equation of the line is known

2- check whether your inequality will have an equal sign or not:

To do this, check the graphed line:

i. if it is a solid line, then the inequality will have an equal sign (≤ or ≥)

ii. if it is a dashed line, then the inequality will not have an equal sign (< or >)

3- Final step is to get the inequality:

To do this, take any point from the shaded region, substitute with it in the equation of the line and then check whether the calculated y value is greater or less than the value of the y of the chosen point. This way, you will be able to identify the sign of the inequality.

Hope this helps :)