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

The slope $$m$$ between two points $$(x_1, y_1)$$ and $$(x_2, y_2)$$ is calculated using the formula: $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ .

The slope of a horizontal line is 0.

The slope of a vertical line is undefined.

A positive slope indicates that as the x-value increases, the y-value also increases, resulting in an upward slant from left to right.

A negative slope indicates that as the x-value increases, the y-value decreases, resulting in a downward slant from left to right.

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

Substitute -5 for b: $$3(-5) + 14 = -15 + 14 = -1$$ .

If you have a slope $$m$$ and a point $$(x_1, y_1)$$ , you can find the y-intercept $$b$$ using the formula: $$b = y_1 - mx_1$$ .