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.