Point-Slope Form Notes

Point-Slope Form Definition

  • Point-slope form defines a linear equation using a known point (x1,y1)(x_1, y_1) and a slope mm.
  • The standard point-slope form equation is: y−y1=m(x−x1)y - y_1 = m(x - x_1)
  • Components of the equation:
    • mm represents the slope of the line.
    • (x1,y1)(x_1, y_1) represents the x-coordinate and y-coordinate of a specific point on the line.
    • xx and yy represent the general variables of the line equation.

Converting to Slope-Intercept Form

  • Slope-intercept form equation: y=mx+by = mx + b
  • To convert an equation from point-slope form to slope-intercept form:
    • Distribute the slope mm across (x−x1)(x - x_1).
    • Isolate yy by adding or subtracting y1y_1 on both sides of the equation.

Writing Equations Given Two Points

  • When given two points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2), determine the slope mm first using the slope formula: m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}
  • Substitute the calculated slope mm and either point (x1,y1)(x_1, y_1) or (x2,y2)(x_2, y_2) into the point-slope equation y−y1=m(x−x1)y - y_1 = m(x - x_1).
  • Choosing either point yields an equivalent equation for the line.