cartesian plane maths test revison

Main equation for a straight line

y = mx + c, where y is the vertical position, m is the gradient/slope, x is the horizontal position, and c is the y-intercept.

Gradient

The slope of a line, calculated as rise ÷ run, indicating how steep the line is.

Y-intercept

The point where the line crosses the Y-axis; determined by the value of c in the equation y = mx + c.

X-intercept

The point where the line crosses the X-axis; found by setting y = 0 in the equation.

Finding gradient from two points

Using points (x₁, y₁) and (x₂, y₂) in the formula m = (y₂ - y₁) ÷ (x₂ - x₁).

Drawing a line from an equation

Start at c, use the gradient to find another point, and draw the line through these points.

Finding an equation from two points

Calculate the gradient using m = (y₂ - y₁) ÷ (x₂ - x₁), then substitute a point into y = mx + c to find c.

Word problems

Real-life scenarios that can be represented with equations, identifying starting amounts as c and changes as m.

Parallel Lines

Lines that never meet and have the same gradient.

Perpendicular Lines

Lines that intersect at a 90° angle, with gradients being negative reciprocals of each other.

Intersection

The point where two lines meet, found by solving their equations together.

Simultaneous Equations Graphically

Finding the solution to two equations by drawing their lines and determining the intersection point.