Linear Equations & Graphs
Straight lines, gradients and y-intercepts
Master linear equations in the form y = mx + c and draw straight line graphs.
📖 Understanding Linear Equations & Graphs
A linear equation produces a straight line when graphed. The standard form is y = mx + c, where m is the gradient (slope) and c is the y-intercept (where the line crosses the y-axis).
The gradient (m) measures the steepness of the line. m = rise/run = (y₂−y₁)/(x₂−x₁). Positive gradient goes up left to right; negative gradient goes down.
Two lines are parallel if they have the same gradient. Two lines are perpendicular if their gradients multiply to −1 (m₁ × m₂ = −1).
Simultaneous equations are two equations with two unknowns. We solve them by substitution or elimination to find values of x and y that satisfy both.
🔑 Key Points to Remember
- ✓y = mx + c: m = gradient, c = y-intercept
- ✓Gradient = (y₂−y₁)/(x₂−x₁)
- ✓Parallel lines: same gradient
- ✓Perpendicular lines: m₁ × m₂ = −1
- ✓Simultaneous equations: solve by substitution or elimination
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