Point-Slope Form

The point-slope form of a linear equation is given by the formula: y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

To convert from point-slope form (y - y1 = m(x - x1)) to slope-intercept form (y = mx + b), solve for y to isolate it on one side of the equation.

The slope of a line is a measure of its steepness, calculated as the change in y (rise) divided by the change in x (run) between two points on the line.

The slope (m) between two points is calculated using the formula: m = (y2 - y1) / (x2 - x1).

The slope-intercept form of a linear equation is expressed as y = mx + b, where m is the slope and b is the y-intercept.

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

In the equation y = mx + b, the slope (m) is the coefficient of x.

The point (x1, y1) represents a specific point on the line, which is used as a reference to write the equation in point-slope form.

To write the equation of a line given a point (x1, y1) and a slope m, use the point-slope form: y - y1 = m(x - x1).

Point-slope form can be converted to slope-intercept form by solving for y, allowing for easier identification of the slope and y-intercept.