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

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.

Step-by-step 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.

Graphing Systems of Linear Inequalities. To graph a linear inequality in two variables (say, x and y ), first get y alone on one side. ... If the inequality is strict ( < or > ), graph a dashed line. If the inequality is not strict ( ≤ or ≥ ), graph a solid line.

Step-by-step explanation:

Step-by-step explanation:

You first need to determine the individual inequalities according to their shading. The perfectly vertical line is at x = -2. However, since this is an inequality and there is shading involved, we have to use an inequality sign that signifies which side of the line is shaded. We are shading to the left of the line and those values are less than -3. BUT we also have a dotted line as opposed to a solid line. That inequality, then, looks like this:

x < -3

The other inequality is a line. It is solid, and the solution set is below the line so those values are also less than the line. First, determine what the equation for the line is, then we will worry about the inequality. The y-intercept is at -2, and the slope is -1, so the inequality is:

y ≤ -x - 2

The system is both of those inequalities put together.

The system of linear inequalities to each graph is the following

1) (Largest graph)

(1) y≤-3x

(2) y≥2x-4

2) (Smallest graph)

(1) y≤x+2

(2) y≤-x-3

Step-by-step explanation:

1) Largest graph

We can see two right lines

a) One of the lines (Line 1) goes through:

Origin: O=P1=(0,0)=(x1, y1)→x1=0, y1=0

P2=(2, -6)→x2=2, y2=-6

Slope line 1: m1=(y2-y1)/(x2-x1)

Replacing the known values:

m1=(-6-0)/(2-0)

m1=(-6)/(2)

m1=-3

Equation line 1:

y-y1=m1 (x-x1)

y-0=-3(x-0)

y=-3x

The region is below this right line, then the first inequality is:

(1) y≤-3x

b) The other line (Line 2) goes through:

P3=(2,0)=(x3, y3)→x3=2, y3=0

P4=(5, 6)→x4=5, y4=6

Slope line 2: m2=(y4-y3)/(x4-x3)

Replacing the known values:

m2=(6-0)/(5-2)

m2=(6)/(3)

m2=2

Equation line 2:

y-y3=m2 (x-x1)

y-0=2(x-2)

y=2x-4

The region is above this right line, then the second inequality is:

(2) y≥2x-4

Then, the system of linear inequalities for the largest graph is:

(1) y≤-3x

(2) y≥2x-4

2) Smallest graph

We can see two right lines

a) One of the lines (Line 1) goes through:

P1=(0, 2)=(x1, y1)→x1=0, y1=2

P2=(5, 7)→x2=5, y2=7

Slope line 1: m1=(y2-y1)/(x2-x1)

Replacing the known values:

m1=(7-2)/(5-0)

m1=(5)/(5)

m1=1

Equation line 1:

y-y1=m1 (x-x1)

y-2=1(x-0)

y-2=1(x)

y-2=x

y-2+2=x+2

y=x+2

The region is below this right line, then the first inequality is:

(1) y≤x+2

b) The other line (Line 2) goes through:

P3=(0,-3)=(x3, y3)→x3=0, y3=-3

P4=(5, -8)→x4=5, y4=-8

Slope line 2: m2=(y4-y3)/(x4-x3)

Replacing the known values:

m2=(-8-(-3))/(5-0)

m2=(-8+3)/(5)

m2=(-5)/5

m2=-1

Equation line 2:

y-y3=m2 (x-x1)

y-(-3)=-1(x-0)

y+3=-1(x)

y+3=-x

y+3-3=-x-3

y=-x-3

The region is below this right line, then the second inequality is:

(2) y≤-x-3

Then, the system of linear inequalities for the smallest graph is:

(1) y≤x+2

(2) y≤-x-3