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# Pc8 6 parametric equations

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### Pc8 6 parametric equations

1. 1. Vectors and Parametric Equations Precalculus 8-6 p. 520
2. 2. Vector Equations <ul><li>A line through a point which is parallel to the vector is defined by the set of points and such that the vector is a scalar multiple of </li></ul>
3. 3. Parametric Equations <ul><li>A line through that is parallel to has the following parametric equations, where t is any real number (scalar). </li></ul>
4. 4. Parametric Equations <ul><li>A line through that is parallel to has the following parametric equations, where t is any real number (scalar). </li></ul>
5. 5. Parametric Equations <ul><li>Note that each value of t establishes an ordered pair (x, y) that is a point on the line. </li></ul>
6. 6. Parametric  Slope-Intercept Form <ul><li>Given Slope-Intercept Form: </li></ul><ul><ul><li>x is the independent variable, and y is the dependent variable. </li></ul></ul>
7. 7. Parametric  Slope-Intercept Form <ul><li>Given Slope-Intercept Form: </li></ul><ul><ul><li>x is the independent variable, and y is the dependent variable. </li></ul></ul><ul><ul><li>In parametric equations, t is the independent variable, and both x and y are dependent on t . </li></ul></ul>
8. 8. Parametric  Slope-Intercept Form <ul><li>Given Slope-Intercept Form: </li></ul><ul><ul><li>x is the independent variable, and y is the dependent variable. </li></ul></ul><ul><ul><li>In parametric equations, t is the independent variable, and both x and y are dependent on t . </li></ul></ul><ul><ul><li>If we set the independent variables x and t equal, we can write two parametric equations in terms of t . </li></ul></ul>
9. 9. Parametric  Slope-Intercept Form <ul><li>Given: Parametric Equations </li></ul><ul><ul><li>Solve both equations for t . </li></ul></ul>
10. 10. Parametric  Slope-Intercept Form <ul><li>Given: Parametric Equations </li></ul><ul><ul><li>Solve both equations for t . </li></ul></ul><ul><ul><li>Set the equations equal to each other. </li></ul></ul>
11. 11. Parametric  Slope-Intercept Form <ul><li>Given: Parametric Equations </li></ul><ul><ul><li>Solve both equations for t . </li></ul></ul><ul><ul><li>Set the equations equal to each other. </li></ul></ul><ul><ul><li>Solve for y (put in slope-intercept form). </li></ul></ul>