Straight Line Graphs — NSW Year 10 Core Maths
Length, midpoint and gradient of an interval, parallel and perpendicular lines, and equations of lines. Five subtopics and 100 practice questions, each with a worked solution, aligned to NESA MA5-LIN-C-01 and MA5-LIN-C-02.
Straight Line Graphs in NSW Year 10 Core
Straight line graphs bring algebra and the number plane together. In Year 10 Core, students find the length, midpoint and gradient of an interval joining two points, use gradients to recognise parallel and perpendicular lines, and write a line's equation as \(y = mx + c\) and in general form.
The five subtopics below build in that order, from the length of an interval to finding equations of lines. Straight Line Graphs is one of the 11 topics in NSW Year 10 Maths Core and sits within NESA's Number and Algebra strand (NESA outcomes MA5‑LIN‑C‑01 and MA5‑LIN‑C‑02, with general form from MA5‑LIN‑P‑01). The topic leads on to the coordinate geometry of Stage 6.
Subtopics
Straight Line Graphs: common questions
How do you find the gradient of a line?
Divide the rise by the run between two points on the line. For example, the gradient through \((-3, -5)\) and \((1, 7)\) is \(\frac{7 - (-5)}{1 - (-3)} = \frac{12}{4} = 3\).
How do you find the midpoint of an interval?
Average the \(x\)-coordinates and average the \(y\)-coordinates. The midpoint of \((6, 9)\) and \((-2, 7)\) is \(\left(\frac{6 + (-2)}{2}, \frac{9 + 7}{2}\right) = (2, 8)\).
How can you tell if two lines are perpendicular?
Multiply their gradients. If the product is \(-1\), the lines are perpendicular; for example, gradients \(2\) and \(-\frac{1}{2}\). Parallel lines have equal gradients.
Which NESA outcomes cover straight line graphs in Year 10?
Length, midpoint and gradient of an interval come under MA5‑LIN‑C‑01, and the form y = mx + c with perpendicular lines under MA5‑LIN‑C‑02. Writing lines in general form belongs to the Path outcome MA5‑LIN‑P‑01.
What does y = mx + c mean?
It is the gradient–intercept form of a straight line. \(m\) is the gradient and \(c\) is where the line crosses the \(y\)-axis, so \(y = 9 - 7x\) has gradient \(-7\) and \(y\)-intercept \(9\).