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Exercises Graphs and straight lines

Example 4.69 from Elementary Algebra, 4.7 Graphs of Linear Inequalities

Graphs of Linear Inequalities: example 4.69

Determine whether each ordered pair is a solution to the inequality $y > x + 4$ :

ⓐ $(0, 0)$ ⓑ $(1, 6)$ ⓒ $(2, 6)$ ⓓ $(−5, −15)$ ⓔ $(−8, 12)$

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

1
Solution
1. ⓐ
  
  $(0, 0)$
  
  Simplify.
  So, $(0, 0)$ is not a solution to $y > x + 4$ .
2. ⓑ
  
  $(1, 6)$
  
  Simplify.
  So, $(1, 6)$ is a solution to $y > x + 4$ .
3. ⓒ
  
  $(2, 6)$
  
  Simplify.
  So, $(2, 6)$ is not a solution to $y > x + 4$ .
4. ⓓ
  
  $(−5, −15)$
  
  Simplify.
  So, $(−5, −15)$ is not a solution to $y > x + 4$ .
5. ⓔ
  
  $(−8, 12)$
  
  Simplify.
  So, $(−8, 12)$ is a solution to $y > x + 4$ .

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Determine whether each ordered pair is a solution to the inequality $y > x - 3$ :

ⓐ $(0, 0)$ ⓑ $(4, 9)$ ⓒ $(−2, 1)$ ⓓ $(−5, −3)$ ⓔ $(5, 1)$

How did it go?

PreviousFind the Equation of a Line: example 4.68 Next Graphs of Linear Inequalities: example 4.70

From Elementary Algebra (1st edition) by OpenStax (Rice University), section 4.7, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.