Finding Equations of Lines

learning_notes

Last updated: 8/16/2025

Key Concepts:

  • The equation of a line can be determined when given two points or one point and a slope.
    • When given a point ((x_1, y_1)) and slope m: use the point-slope form (y - y_1 = m(x - x_1)).
    • When given two points ($x_1, y_1$) and ($x_2, y_2$): find the slope using (m = \frac{y_2 - y_1}{x_2 - x_1}), then use point-slope form to find the y-intercept.
  • Rearranging Forms: Linear equations can be converted into (y = mx + b) for easier graphing.

Skills Covered:

  • Writing the equation of a line given a point and slope.
  • Finding the equation of a line passing through two points.
  • Converting equations to slope-intercept form.

Example Problems:

  • Find the equation of a line passing through ((4, -1)) with a slope of 3.
  • Find the equation of a line that passes through ((-2, 5)) and ((3, -4)).
  • Rewrite (6x - 2y = 8) in slope-intercept form.

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