Linear Functions: Standard Form

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

To convert $$y = mx + b$$ to standard form, rearrange it to the form $$Ax + By = C$$ by moving all terms involving variables to one side.

The slope of a line represents the rate of change of y with respect to x, indicating how steep the line is.

The y-intercept is the point where the line crosses the y-axis, represented by the value of y when x = 0.

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

Parallel lines have the same slope, meaning they never intersect and have identical steepness.

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

Use the point-slope form $$y - y1 = m(x - x1)$$ , where (x1, y1) is the point and m is the slope.

Add y to both sides to get $$y = -x - 3$$ , then rearrange to standard form.

Start with $$y = mx + b$$ , substitute the slope and y-intercept, then rearrange to standard form.