How to Write a Linear Inequality from a Graph?

How to write a linear inequality from a graph, step by step: the rule in plain language, solved examples worked one line at a time, and practice questions so you can try it yourself before moving on.

Step 1: Identify the slope and (y)-intercept of the line

Step 2: Determine whether the line is solid or dashed

Step 3: Determine whether the inequality is “greater than” or “less than

Step 4: Write the inequality using (“y”) for the (y)-coordinate and (“x”) for the (x)-coordinate

Step 5: Write the final inequality

Writing a Linear Inequality from a Graph, Examples 1

Solution:

Now consider (2) points on the solid line to find the slope. You can use ((0,3)) and ((-2,-1)):

(m=frac{(y_2, y_1)}{(x_2, x_1)}=frac{-1-3}{-2-0}=frac{-4}{-2}=2→m=2).

Now use the value of (b) and (m) and put them into the slope-intercept form formula: (y=mx+b→y=2x+3).

Determine the symbol of inequality: you have a solid line and the shaded part is above the line. So, the equation of the inequality is as follows: (y≥2x+3).

Exercises for Writing a Linear Inequality from a Graph

Write the slope-intercept form equation of the following graph.

1.

2.

1. (color{blue}{y≥3x+7})
2. (color{blue}{y<2x+12})

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