Multiple Representations 2

A linear equation is an equation that makes a straight line when graphed. It can be written 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 y-value with respect to the x-value. It indicates how steep the line is.

The y-intercept is the point where the line crosses the y-axis. It is represented by the value of $$b$$ in the equation $$y = mx + b$$ .

Use the point-slope form of the equation: $$y - y_1 = m(x - x_1)$$ , where $$m$$ is the slope and $$(x_1, y_1)$$ is the point.

The independent variable is the variable that is changed or controlled in an experiment (usually x), while the dependent variable is the variable that is measured or affected (usually y).

A relationship can be represented using a table by listing pairs of values for the independent and dependent variables, showing how one variable affects the other.

A function is a relation that assigns exactly one output for each input. In other words, for every x-value, there is one corresponding y-value.

A graph is linear if it forms a straight line. This indicates a constant rate of change between the variables.

An equation is linear if it can be written in the form $$y = mx + b$$ , where $$m$$ and $$b$$ are constants.

The coefficients in a linear equation determine the slope and the y-intercept, which affect the steepness and position of the line on the graph.