Graphing Linear Equations

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 represented by the value of $$b$$ in the equation $$y = mx + b$$ .

The slope (m) can be calculated using the formula $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ , where (x1, y1) and (x2, y2) are the coordinates of the two points.

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

A positive slope indicates that as x increases, y also increases, resulting in an upward slant of the line.

A negative slope indicates that as x increases, y decreases, resulting in a downward slant of the line.

The standard form of a linear equation is $$Ax + By = C$$ , where A, B, and C are integers, and A should be non-negative.

To graph a linear equation, you can find the y-intercept and slope, plot the y-intercept on the graph, and use the slope to find another point.

The slope indicates the steepness and direction of the line, while the y-intercept is the point where the line crosses the y-axis.