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Linear Equations Flashcards
GCSE Mathematics (Edexcel) 1MA1
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Linear equation
An equation that forms a straight line when graphed. It has the general form y = mx + c.
Gradient (m) in y = mx + c
The steepness of the line, representing the rate of change. It is the coefficient of x.
Y-intercept (c) in y = mx + c
The point where the line crosses the y-axis. It is the constant term in the equation.
Solving a linear equation
Find the value of the variable that makes the equation true by isolating the variable.
Equation of a horizontal line
y = c, where c is a constant. The gradient (m) is 0.
Equation of a vertical line
x = a, where a is a constant. The gradient is undefined.
Parallel lines
Lines that have the same gradient (m) but different y-intercepts (c).
Perpendicular lines
Lines whose gradients multiply to give -1 (m₁ × m₂ = -1).
Finding the gradient from two points
Use the formula m = (y₂ - y₁) / (x₂ - x₁).
Rearranging to y = mx + c form
Manipulate the equation to isolate y on one side, ensuring it is in the form y = mx + c.
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