Slope intercept form: the equation for a line is y = mx + b, where m = slope and b is the y-intercept. Parallel lines have the same slope. You are given y = 2x + 2, the slope of this line is 2. So the slope of the unknown line is also 2. You are also given a point on the unknown line, (-1,3). Solve for the unknown line by using m = 2, x = -1 ...

Example 2 Determine if the line that passes through the point (0,−3,8) (0, − 3, 8) and is parallel to the line given by x = 10+3t x = 10 + 3 t, y = 12t y = 12 t and z =−3−t z = − 3 − t passes through the xz x z -plane. If it does give the coordinates of that point.

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