Chapter 6 - Systems of Equations and Inequalities - Concept Byte - Graphing Linear Inequalities - Page 402: 2

y $\geq$ 3x+3 y $\lt$ -x-2

Work Step by Step

Looking at the solid line, we can see that the y-intercept is 3. We can also tell that the slope is 3. Remember that slope is rise over run. You also need to remember that a solid line means "or equal to". Because the shaded area is above the line, we know it is greater than. So, with all this knowledge, we come to the conclusion that the equation of the first line is y $\geq$ 3x+3. Now look at the dashed line. We can tell that the y-intercept is -2. Then, we can find the slope once again using rise over run from one point to another. The dashed line means it is not "or equal to". Given that the shaded area is below the line, we know that it is less than. Putting this all together, the equation of this line is y $\lt$ -x-2.

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