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2.2 – Linear Equations and their Intercepts

2.2 – Linear Equations and their Intercepts. Recall…. Linear Equation = equation in the form: ax + by = c Highest Power (Degree) = 1 Non-Linear Equation = an equation in a form other than linear Degree > 1. To tell if an equation is linear: 1) Solve for y

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2.2 – Linear Equations and their Intercepts

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  1. 2.2 – Linear Equations and their Intercepts

  2. Recall… • Linear Equation = equation in the form: • ax + by = c • Highest Power (Degree) = 1 • Non-Linear Equation = an equation in a form other than linear • Degree > 1

  3. To tell if an equation is linear: • 1) Solve for y • 2) Check to see if any higher degree of x’s exist Is the highest degree 1? Yes Non-Linear No Non-Linear

  4. Example. Classify each equation as linear or non-linear. • a) 3x + 2(x+7) – 2y = 5x • b) 4x3 – 2y = 5x • c) x2 – (x – 1)2 = y • d) x2 – 2x = 3 – x2 + y

  5. Intercepts • Any particular equation may or may not cross a particular axis (x or y) • X-Intercept = point where a graph crosses the x-axis • Y-Intercept = point where a graph crosses the y-axis

  6. X-Intercept: when y = 0 • Y-Intercept: when x = 0 • Example. Find the x and y intercepts of the equation 3x – 4y = 12. Then, graph. • Remember: 2 points to make a line!

  7. Example. Find the x and y intercepts of the equation 2x – 3 = 1 – 4y. The, graph.

  8. Vertical and Horizontal Lines • Vertical Lines: always have an x=intercept, only • x = a • Horizontal Lines: always have a y-intercept, only • y = a

  9. Example. Graph y = -5. • Example. Graph x = 4.

  10. Assignment • Pg. 145 • 1-7 odd, 21-24, 25-31 odd, 38, 39

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