Linear Functions

The Point-Slope Form is given by the equation: $$y - d = m(x - c)$$ , where (c, d) is a point on the line and m is the slope.

The Slope-Intercept Form is given by the equation: $$y = mx + b$$ , where m is the slope and b is the y-intercept.

The slope (m) represents the rate of change of y with respect to x; it indicates how steep the line is.

The y-intercept (b) is the value of y when x = 0; it is the point where the line crosses the y-axis.

To convert from Slope-Intercept Form $$y = mx + b$$ to Standard Form $$Ax + By = C$$ , rearrange the equation to isolate terms.

The Standard Form is given by the equation: $$Ax + By = C$$ , where A, B, and C are integers, and A should be non-negative.

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

A positive slope indicates the line rises, a negative slope indicates it falls, a zero slope indicates a horizontal line, and an undefined slope indicates a vertical line.

Parallel lines have the same slope but different y-intercepts.

Perpendicular lines have slopes that are negative reciprocals of each other; if one slope is m, the other is $$-\frac{1}{m}$$ .