6.6C - Multiple Representations

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 y with respect to x. It indicates how steep the line is and the direction it goes (upward or downward).

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

An additive relationship can be identified by a straight line that shows a constant increase or decrease in y as x increases. The difference between consecutive y-values remains constant.

A table of values lists pairs of x and y values that satisfy a linear equation. It helps to visualize the relationship between the variables.

To determine if a graph represents the equation $$y = 2x$$ , check if for every x-value, the corresponding y-value is double that x-value.

An additive relationship involves adding a constant to get from one y-value to the next, while a multiplicative relationship involves multiplying a constant to get from one y-value to the next.

The equation $$y = x + 5$$ represents a linear relationship where for every increase of 1 in x, y increases by 1, starting from 5 when x is 0.

To find the equation of a line from a graph, identify the slope (rise over run) and the y-intercept, then use the slope-intercept form $$y = mx + b$$ .

A graph of a proportional relationship is a straight line that passes through the origin (0,0) and has a constant slope.