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2.2 – Linear Equations and their Intercepts

This resource covers the fundamentals of linear equations, identifying their form, and distinguishing them from non-linear equations. You’ll learn how to determine linearity by solving for y and checking the highest degree of the variable. The document also explains x and y intercepts, providing examples to find these points and graph the equations. Additionally, it discusses the characteristics of vertical and horizontal lines. Ideal for students looking to solidify their understanding of linear equations and their graphical representations.

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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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