Question

How would you write a system of linear inequalities from a graph?

Answer 1

Explanation:

You need to know how to write a linear equation from its graph.

A graphed system of linear inequalities will have 2 lines. Each line may be solid or dashed. In addition, there is shading on one side of each line.

For each line, do this:

First, find the equation of the line.

Second, if the line is solid, you will use >= or <= instead of the equal sign. If a line is dashed, you will use < or > instead of the equal sign.

To find out whether the sign is greater than or less than, guess one of the two signs. Then test a point on the shaded side. If the point works in the inequality, you guessed correctly. If it does not work, reverse the symbol.

Do this for each inequality.

Answer 2

First, take two points from the graph. Call these points (a, b) and (c, d).

Next, find the slope. You can find this by doing (b-d)/(a-c).

Call the slope m. You will need this later.

Make an equation in slope intercept form (y = mx + b).

Now, take one of the points, and plug it into the equation.

mx + b has the same m as the slope.

From here, you can figure out b (the y-intercept).

To make a system, you do the same thing, but find where it is greater and lower.