GCSE Maths Practice: coordinates

Question 8 of 10

This question reinforces calculating the gradient between two points.

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\( \begin{array}{l}\text{What is the gradient of the line joining the points } (1,2) \text{ and } (5,6)?\end{array} \)

Choose one option:

Subtract y-values, subtract x-values, divide. Check by plotting points.

Calculate the gradient by subtracting the y-coordinates, subtracting the x-coordinates, and dividing the results: m=(y2-y1)/(x2-x1). For example, points (1,2) and (5,6) give m=(6-2)/(5-1)=4/4=1. The gradient indicates the slope and direction of the line. Understanding this helps in plotting lines, finding equations, and solving related coordinate geometry problems. Practicing with integer, fractional, positive, negative, and zero slopes strengthens comprehension and graphing skills. Accurate gradient calculations are foundational for problems involving parallel and perpendicular lines, line intersections, and real-world applications in design, navigation, and physics. Always check your calculation by plotting points to verify the gradient.