GCSE Maths Practice: coordinates

Question 4 of 10

This question shows how to find the x-coordinate when a point lies on a line.

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\( \begin{array}{l}\text{Find the value of } x \text{ if the point } (x,4) \text{ lies on the line } y=2x+1.\end{array} \)

Choose one option:

Substitute the known value, isolate x, solve carefully, check by substitution.

When given a linear equation and one coordinate of a point, you can find the unknown coordinate by substituting the known value into the equation. For example, with y=2x+1 and y=4, substitute 4 for y: 4=2x+1. Solve for x by subtracting 1: 3=2x. Divide by 2 to get x=1.5. This process reinforces understanding of linear relationships and algebraic manipulation. It's important to check the solution by substituting x back into the equation: y=2*1.5+1=4, which confirms the solution. This technique is widely applicable in coordinate geometry, including finding intersection points, solving parallel and perpendicular line problems, and analyzing real-life situations such as rate-distance-time problems or interpreting graphs. Practicing with various equations, including negative gradients and fractional coefficients, helps build fluency. Understanding how to isolate variables in equations is a fundamental algebra skill required throughout GCSE Maths and further mathematics studies.