Flashcard 2 - Next Generation Advanced Algebra and Functions Flashcard Set for the ACCUPLACER Test

standard form: \(Ax + By + C = 0\), where A, B, and C are constants.
slope-intercept form: \(y = mx + b\), where m is the slope, defined as \(m = \frac{y_2 - y_1}{x_2 - x_1}\), where \((x_1, y_1)\) and \((x_2, y_2)\) are two points on the line, and b is the y-intercept.
point-slope form: \((y - y_1) = m(x - x_1)\), where m is the slope, and \((x_1, y_1)\) is a point on the line.
Parallel lines share the same slope. Intersecting lines have different slopes, and in the special case where the slopes are negative reciprocals of each other, the lines are perpendicular (they intersect at a \(90^\circ\) angle).

A linear equation directly relates an output variable to an input variable. Non-vertical lines exhibit a slope, which is the constant ratio of the change in output values to the input values, and a y-intercept, which is the point at which the line passes through the y-axis. Vertical lines exhibit an undefined slope because the change in input values is 0, but have an x-intercept, which is the point at which the line passes through the x-axis. Given 2 points, or a point and a slope, the equation to the line can be produced.