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 the y-value with respect to the x-value. It indicates how steep the line is.

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

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

A zero slope indicates that the line is horizontal, meaning there is no change in the y-value as the x-value changes.

The x-intercept is the point where the line crosses the x-axis. It can be found by setting $$y = 0$$ in the equation and solving for $$x$$ .

The y-intercept is the value of $$b$$ in the equation, which is $$4$$ .

The slope of the line is $$2$$ .

The slope is calculated as $$m = \frac{{1 - (-4)}}{{3 - 2}} = 5$$ .

A negative slope indicates that the line is decreasing, meaning as the x-value increases, the y-value decreases.