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 of a line, typically in the form $$y = mx + b$$ , where $$m$$ is the slope and $$b$$ is the y-intercept.

The slope of a line 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 one-unit increase in x.

The slope (m) can be calculated using the formula: $$m = \frac{y2 - y1}{x2 - x1}$$ .

The y-intercept is the value of y when x is 0. It is the point where the line crosses the y-axis.

The slope-intercept form of a linear equation is $$y = mx + b$$ , where $$m$$ is the slope and $$b$$ is the y-intercept.

This equation represents a linear relationship where the slope is -2 and the y-intercept is 4. The line decreases as x increases.

A slope of 5 means that for every 1 unit increase in x, y increases by 5 units.

The y-intercept can be found by identifying the value of y when x is 0 in the table.

This equation represents a situation where a person starts with $800 and loses $30 each month, showing how savings decrease over time.

To graph a linear equation, identify the y-intercept, plot it on the graph, and use the slope to find another point. Draw a straight line through these points.