Point Slope Form Standard Form

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Presentation transcript:

Point Slope Form Standard Form Writing Equations of Lines Point Slope Form Standard Form

Point Slope Form Variable Variable y – y1 = m(x – x1) Slope (x1, y1)

Steps Write the equation: Determine the slope Substitute slope for “m” Substitute values from a point for x1 and y1 Eliminate any “double signs” (i.e. +-, --, etc.)

Why does the point-slope form work? Find the slope between (x1, y1) and (x, y). Reflexive property Point-Slope Form

Write the equation of the line with slope 3 and passing through the point (1, 5). Use Point-Slope Form y – y1 = m(x – x1)

Write the equation of the line with slope ¾ and passing through the point (-5, 3). Use Point-Slope Form y – y1 = m(x – x1)

Write the equation of the line with slope -2/3 and passing through the point (2, -4). y – y1 = m(x – x1)

Find the slope let's use (3, -1) Write the equation of the line passing through the points (-2, 6) and (3, -1). Find the slope y – y1 = m(x – x1) let's use (3, -1)

Find the slope let's use (4, 3) Write the equation of the line passing through the points (4, 3) and (6, 8). Find the slope y – y1 = m(x – x1) let's use (4, 3)

Find the slope let's use (4, -3) Write the equation of the line passing through the points (4, -3) and (-7, -1). Find the slope y – y1 = m(x – x1) let's use (4, -3)

Standard Form Constant Both Can’t Be 0 Integer When Possible Any Constant

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Convert y = 3x + 2 to standard form. multiply both sides by -1

Convert y = 6776x to standard form. multiply both sides by -4

Convert y = 6776x to standard form. multiply both sides by 7

Convert y = 6776x to standard form. multiply both sides by -2

Convert y = 6776x to standard form. multiply both sides by 15

More on Slope Parallel lines have the same slope Perpendicular lines have opposite reciprocal slopes Parallel Lines Perpendicular Lines

What is the slope of the given line? Write the equation of the line parallel the line 4x – 5y = 7 that passes through the point (-3, 7) What is the slope of the given line? y – y1 = m(x – x1)

What is the slope of the given line? Write the equation of the line perpendicular the line 3x + 2y = 9 that passes through the point (2, 5) What is the slope of the given line? y – y1 = m(x – x1)