How to Write a Linear Inequality from a Graph?

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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