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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 – 2) Check to see if any higher degree of x’s exist Is the highest degree 1? Yes NoNon-Linear
Example. Classify each equation as linear or non-linear. a) 3x + 2(x+7) – 2y = 5x b) 4x 3 – 2y = 5x c) x 2 – (x – 1) 2 = y d) x 2 – 2x = 3 – x 2 + y
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
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!
Example. Find the x and y intercepts of the equation 2x – 3 = 1 – 4y. The, graph.
Vertical and Horizontal Lines Vertical Lines: always have an x=intercept, only x = a Horizontal Lines: always have a y-intercept, only y = a
Example. Graph y = -5. Example. Graph x = 4.
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I can graph linear equations using intercepts and write linear equations in standard form.
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