Straight Line — NSW Year 9 Core Maths
Length, midpoint and gradient of an interval, graphing lines, y = mx + c, finding equations and solving with graphs. Seven subtopics and 140 practice questions with worked solutions, aligned to MA5-LIN-C-01 and MA5-LIN-C-02.
Straight Line in NSW Year 9
Straight Line is coordinate geometry: working with points and lines on the number plane. Year 9 Core students find the length, midpoint and gradient of an interval from the coordinates of its ends, graph lines from tables and intercepts, use \(y = mx + c\), the gradient-intercept form, to read and write equations, and find a line running parallel to another line or meeting it at right angles.
The seven subtopics below cover the length of an interval, midpoints, the gradient of a line, graphing linear equations, the gradient-intercept equation, finding the equation of a line, and solving linear equations graphically. Straight Line is one of the 13 topics in NSW Year 9 Core Maths and belongs to the Number and Algebra strand. Length, midpoint, gradient and graphing are Stage 5 Core content under NESA outcome MA5‑LIN‑C‑01, the gradient-intercept form under MA5‑LIN‑C‑02, and solving with graphs revises MA4‑LIN‑C‑01. Straight lines lead on to simultaneous equations and to the curved graphs of non-linear relationships in Year 10.
Subtopics
Straight Line: common questions
How do you find the length of an interval?
Find the run and the rise between the two points, then use Pythagoras' theorem. From \((3,-2)\) to \((-12,6)\) the run is \(15\) and the rise is \(8\), so the length is \(\sqrt{15^2 + 8^2} = \sqrt{289} = 17\) units.
How do you find the midpoint of an interval?
Average the \(x\)-coordinates and average the \(y\)-coordinates. The midpoint of \((-3,5)\) and \((7,9)\) is \(\left(\frac{-3 + 7}{2}, \frac{5 + 9}{2}\right) = (2, 7)\).
How do you find the gradient of a line?
Divide the rise by the run between two points on the line. Through \((-2,-2)\) and \((1,4)\), the rise is \(6\) and the run is \(3\), so the gradient is \(m = \frac{6}{3} = 2\). Lines sloping down to the right have negative gradients.
What do m and c mean in y = mx + c?
\(m\) is the gradient, which tells you how steep the line is, and \(c\) is the \(y\)-intercept, where the line crosses the \(y\)-axis. The line \(y = -5x + 2\) has gradient \(-5\) and crosses the \(y\)-axis at \((0, 2)\).
Which NESA outcomes cover straight-line graphs in Year 9?
The length, midpoint and gradient of an interval and graphing linear relationships come under the Stage 5 Core outcome MA5‑LIN‑C‑01. The gradient-intercept form, and parallel and perpendicular lines, come under MA5‑LIN‑C‑02. Solving equations with graphs revises the Stage 4 outcome MA4‑LIN‑C‑01.