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Prerequisite – P.2 and P.3

Learn to graph points, find distances, and write circle equations. Solve linear equations, inequalities, and verify right triangles using Pythagorean Theorem. Understand midpoints, absolute value, and solutions in equations. Practice exercises included.

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Prerequisite – P.2 and P.3

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  1. Prerequisite – P.2 and P.3

  2. Objective • SWBAT graph points, find distances and midpoint on a number line and in a coordinate plane, and write standard-form equations of circles. • SWBAT solve linear equations and inequalities in one variable.

  3. Absolute Value • Absolute Value: the distance between two values on a number line • example: • example: • example: • The distance between x and 12 is less than 15 can be written as

  4. Quadrant names

  5. Midpoint • Midpoint: given two points (( the midpoint formula is • Example: (-3,4) (1,0)

  6. Distance • Distance: given two points (( the distance formula is • Example: (-3,4) (1,0)

  7. Equation of a Circle • Equation of a Circle: a circle is a set of points a fixed distance (radius) from a fixed point (center). • Standard form Equation of a Circle where r is the radius and (h,k) is the center: • Example: Center (-4, 1) radius 8 • Equation:

  8. Converse of the Pythagorean Theorem • Used to verify right triangles • You plug in the three side lengths into the Pythagorean Theorem (and show that is results in a true statement. If the result is not a true statement then the three side lengths do not create a right triangle. • Example: given the side lengths

  9. P.2 HW #1-27 odd, 37, 41-53 odd

  10. Confirming a solution • What does it mean for a number to be a solution to an equation/inequality? • Prove that is a solution of the equation .

  11. Solving Linear Equations

  12. Solving Linear Inequalities

  13. Solving Linear Inequalities with Fractions

  14. Solving Double Inequalities

  15. P.3 HW: #1-53 odd

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