Graphing Linear Inequalities in Two Variables.pptx

Graphing Linear Inequalities in Two Variables.pptx

• 1.
  Graphing Linear Inequalities inTwo Variables Objectives: Graph a linear inequality in two variables. Model a real life situation using a linear inequality.
• 2.
  NOTE:  If thesign is > 𝑜𝑟 <, the line is dashed.  If the sign is ≥ 𝑜𝑟 ≤, the line is solid.  When doing an inequality for just 𝑥.  If the sign is >, shade to the right.  If the sign is <, shade to the left.  When doing an inequality for just 𝑦.  If the sign is >, shade above.  If the sign is <, shade below.
• 3.
  Example: Graph theinequality 𝑦 > 3 on the coordinate plane.
• 4.
  Example: Graph theinequality 𝑥 ≤ −2 on the coordinate plane.
• 5.
  NOTE:  When dealingwith lines that include both variables, 𝑥 𝑎𝑛𝑑 𝑦.  When it is > 𝑜𝑟 ≥, shade above the line.  When it is < 𝑜𝑟 ≤, shade below the line.
• 6.
  EXAMPLES
• 7.
  Graph 𝑦 ≥−3𝑥 + 2 on the coordinate plane. Boundary line: 𝑦 = −3𝑥 + 2 The gradient, 𝑚 = −3. The y-intercept, 𝑐 = 2.
• 8.
  NOTE: For aline of the form 𝑦 = 𝑚𝑥 + 𝑐
• 9.
  Graph 3𝑥 −4𝑦 > 12 on the coordinate plane. Step 1: Rewrite in the form 𝑦 = 𝑚𝑥 + 𝑐. 3𝑥 − 4𝑦 > 12 −4𝑦 > 12 − 3𝑥 𝑦 < 12 − 3𝑥 −4 𝑦 < −3 + 3 4 𝑥 This is the same as 𝒚 < 𝟑 𝟒 𝒙 − 𝟑. Boundary line: 𝑦 = 3 4 𝑥 − 3. The gradient, , 𝑚 = 3 4 . The y-intercept, 𝑐 = −3.
• 10.
  PROBLEM If you haveless than $5.00 in five-cent and ten-cent coins, write an inequality to represent this information. Then draw a graph to describe how many of each type of coin you have. Let 𝑛- number of five-cent coins. Let 𝑑- number of ten-cent coins. 0.05𝑛 + 0.10𝑑 < 5.00 Rewrite as: 𝟓𝒏 + 𝟏𝟎𝒅 < 𝟓𝟎𝟎
• 11.
  Remember: To sketchthe graph of a linear inequality: • Solid Line • Line a small shaded circle on the number line, a solid line indicates that the boundary is included in the solution set. • Dashed Line • Like a small unshaded circle on the number line, a dashed line on the coordinate plane indicates that the boundary is NOT a part of the solution set.