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If you introduce a new variable t (which you can think of as time while you travel along the line), and let that be equal to the three equal expressions above, (x - x1)/a = (y - y1)/b = (z - z1)/c = t then you can solve for x, y, and z to get the parametric equations of the line (expressing x, y, and z in terms of the parameter t): x = at + x1 y = bt + y1 z = ct + z1 This is probably the most-used form.

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Now investigate what happens to the equations of different lines when you translate them left or right. Try to predict what will happen. Explain your findings. Below are the equations of ten lines, and some translations. Each translation links a pair of parallel lines - can you match them up?

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Linear Equations. Find Any Equation Parallel to the Line. in the point-slope form. , which is derived from the slope equation.

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Misc 19 (Method 1) Find the vector equation of the line passing through (1, 2, 3) and parallel to the (3𝑖 ̂ + 𝑗 ̂ + 𝑘 ̂) = 6 . The vector equation of a line passing through a point with position vector...

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Find a parametric equation for the line through (5, 2, 4) parallel to v = 4i + 7j − 9k. Solution Because v1 = −2v2, we conclude that the lines are parallel. Example 0.6. Equation of a plane.

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Find the Equation of a Line Given That You Know a Point on the Line And Its Slope The equation of a line is typically written as y=mx+b where m is the slope and b is the y-intercept. If you a point that a line passes through, and its slope, this page will show you how to find the equation of the line.