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If you need to improve your maths skills, try this quiz on straight lines.

Straight Line (H)

Advance GCSE straight-line graphs: use y = mx + c, parallel and perpendicular gradients, point–slope form, and solve intersections to model real situations.

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Fascinating Fact:

On a street grid, parallel lines share gradients. If L₁ is y = 2x + 1 and L₂ goes through (0, −4) parallel to L₁, then L₂ equals y = 2x − 4.

In GCSE Maths, higher-tier straight-line graphs use y = mx + c to model relationships. You’ll find gradients and intercepts, form equations from points, handle parallel/perpendicular lines, and solve intersections.

Key Terms

Gradient (m): The rate of change; change in y divided by change in x.
y-intercept (c): The value of y when x = 0; where the line meets the y-axis.
Perpendicular gradient: If one line has gradient m, a perpendicular line has gradient −1/m.

Frequently Asked Questions (Click to see answers)

How do I find the equation of a line through a point parallel to y = mx + c?

Use the same gradient m and point–slope form: y − y₁ = m(x − x₁). Substitute the given point, then rearrange to y = mx + c.

How do I find a perpendicular line through a given point?

Find the perpendicular gradient m_? = −1/m, then use y − y₁ = m_?(x − x₁) and rearrange to slope–intercept form.

How do I find the intersection of two straight lines?

Solve the two equations simultaneously. Set them equal (if both are y = ...) or use substitution/elimination to get x and y, which gives the intersection point.