Equation of a Line Flashcards

The equation of a straight line is written as y = mx + c, where m is the gradient and c is the y-intercept.

The gradient of a line is the measure of its steepness, calculated as the change in y divided by the change in x (rise over run).

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

The gradient of a line passing through two points (x₁, y₁) and (x₂, y₂) is calculated as (y₂ - y₁) / (x₂ - x₁).

The equation of a horizontal line is y = c, where c is the constant y-coordinate of all points on the line.

The equation of a vertical line is x = a, where a is the constant x-coordinate of all points on the line.

Parallel lines have the same gradient (m) but different y-intercepts (c).

The gradients of perpendicular lines multiply to give -1. If one line has gradient m, the other has gradient -1/m.

To find the equation of a line, substitute the gradient (m) and a point (x, y) into y = mx + c, then solve for c.

The intercept form of a line is x/a + y/b = 1, where a and b are the x-intercept and y-intercept respectively.