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Understanding Point-Slope Form in Linear Equations

This guide covers the point-slope form of linear equations, defined by the formula y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. Examples include graphing equations like y - 5 = ½(x - 2) and writing equations from given slopes and points, such as slope -3 through (-1, 7). Through these examples, students learn how to graph lines using the point-slope formula and how to derive equations from specific conditions, improving their understanding of linear relationships.

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Understanding Point-Slope Form in Linear Equations

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  1. Point-Slope Form Thursday, November 4, 2010

  2. Formula • y – y1 = m(x – x1) • y1 is the y-coordinate • m is the slope • x1 is the x-coordinate

  3. Graphing Using Point-Slope Form • Graph the equation y – 5 = ½ (x – 2) • The equation shows that the line passes through (2, 5) with slope of ½ . • Start at (2, 5). Using the slope, go up 1 unit and right 2 units to (4,6). Draw a line through the two points.

  4. Graph the equation y – 5 = -⅔(x +2)

  5. Writing an Equation in Point-Slope Form • Write the equation of the line with the slope -3 that passes through the points (-1, 7). • Use the point-slope form • y – y1 = m(x – x1) • Substitute (-1, 7) for (x1, y1) and -3 for m. • y – 7 = -3(x –(-1)) • y – 7 = -3(x + 1)

  6. Write an equation of the line with slope ⅔ that passes through (10,-8). • y + 8 = ⅔(x– 10)

  7. Write an equation of the line with slope 6 that passes through (3,-4). • y + 4 = 6(x– 3)

  8. Write an equation of the line with slope 0 that passes through (-5, 2). • y - 2 = 0(x + 5) • y – 2 = x + 5

  9. Closure • What is the formula for point-slope? • y – y1 = m(x – x1) • What does each piece represent? • y1 is the y-coordinate • m is the slope • x1 is the x-coordinate

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