STAAR - Rate of change/Parallel & Perpendicular

The rate of change is a measure of how much a quantity changes in relation to another quantity. It is often represented as a slope in a linear equation.

The slope of a line is a number that describes the direction and steepness of the line. It is calculated as the change in y divided by the change in x (rise over run).

Two lines are parallel if they have the same slope and will never intersect.

Two lines are perpendicular if the product of their slopes is -1. This means that they intersect at a right angle.

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.

The equation of a line in slope-intercept form is given by y = mx + b, where m is the slope and b is the y-intercept.

Two lines are parallel if their slopes are equal. For example, in the equations y = mx + b1 and y = mx + b2, the lines are parallel.

Two lines are perpendicular if the product of their slopes is -1. For example, if one line has a slope of m1, the other line must have a slope of m2 such that m1 * m2 = -1.

The y-intercept is the point where the line crosses the y-axis. It can be found by setting x = 0 in the equation of the line.

You can use the point-slope form of the equation: y - y1 = m(x - x1), where (x1, y1) is the point and m is the slope.