7th ACA Test 3-2 Review: Linear Relationships

A linear relationship is a relationship between two variables that can be represented by a straight line on a graph. It can be described by the equation y = mx + b, where m is the slope and b is the y-intercept.

The slope (m) in a linear equation represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It indicates how much y changes for a unit change in x.

The y-intercept (b) in a linear equation is the value of y when x is 0. It is the point where the line crosses the y-axis.

y = 3x + 2

A slope of 0 indicates a horizontal line, meaning there is no change in the dependent variable (y) as the independent variable (x) changes. This represents a constant value.

The formula to calculate the slope (m) is m = (y2 - y1) / (x2 - x1).

A relationship is linear if the data points can be plotted on a graph and form a straight line. You can also check if the change in y is consistent for equal changes in x.

Two lines are parallel if they have the same slope but different y-intercepts. This means they will never intersect.

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

y = 25x