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Section 3.2 Connections to Algebra

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In algebra, you learned a system of two linear equations in x and y can have exactly one solution, no solutions, or infinitely many solutions. Geometrically, this means : Intersecting Lines Parallel Lines Coincident Lines

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Postulate 12 If two distinct lines intersect, then their intersection is exactly one point. (think systems of equations)

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Postulate 13 Parallel Postulate If there is a line and a point not on the line, then there is exactly one line through the point parallel to the given line. b ● a

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Example: Line 1 is given by Line 2 is parallel to Line 1 and passes through the point (3,2). Write the equation for Line 2.

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Example 2: is given by is parallel to and passes through the point (1,-1). Write the equation for.

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Postulate 14 Perpendicular Postulate If there is a line and a point not on the line, then there is exactly one line through the point perpendicular to the given line. ● a

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Example: Write the equation of the line which passes through (-1,3) and is perpendicular to Example 2: is given by is perpendicular to and passes through the point (5, -3). Write the equation for.

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More Examples: 1. Solve the following system of equations: x – 2y = -7 3x + 4y = 9 2. Find the equation of a line that is parallel to y = -3x + 2 and passes through the point (2,1). 3. Find the equation of a line that is perpendicular to y = -2x + 1 and passes through the point (4,0).

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More Examples: 4. Write the equation of the line through (-3,2) and (-1,-4). 5. Write in standard form. 6. Write the equation of the line through (-4,4) and (-2,-3) in standard form. 7. Write the equation of the line through (4,9) and (4,5). 8. Write the equation of the line through (-4,-1) and (12,-1).

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