Straight Line Graphs — NSW Year 10 Advanced Maths
Coordinate geometry of straight lines: distance, midpoint and gradient, parallel and perpendicular lines, equations and linear models. Eight subtopics and 160 practice questions with worked solutions, aligned to MA5-LIN-P-01.
Straight Line Graphs in NSW Year 10 Advanced
Straight Line Graphs is coordinate geometry for lines and intervals. Year 10 Advanced students use formulas for the length, midpoint and gradient of an interval, test lines for being parallel or perpendicular with \(m_1m_2=-1\), find and graph equations in gradient–intercept and general form, and use straight-line rules to model real situations.
The eight subtopics below start with the length, midpoint and gradient of an interval, then cover parallel and perpendicular lines, equations of lines and graphing linear equations, and finish with finding an equation from a graph and linear models. Straight Line Graphs is one of the 16 topics in NSW Year 10 Advanced Maths and sits within the Number and Algebra strand (NESA outcomes MA5‑LIN‑C‑02 and MA5‑LIN‑P‑01). These skills lead to simultaneous equations, non-linear graphs and coordinate geometry in Year 11 Advanced.
Subtopics
Straight Line Graphs: common questions
What is the distance formula?
The distance between \((x_1,y_1)\) and \((x_2,y_2)\) is \(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\). For \(L(6,-2)\) and \(M(-2,2)\), \(d=\sqrt{64+16}=\sqrt{80}=4\sqrt{5}\) units.
How do you know if two lines are perpendicular?
Find each gradient. The lines are perpendicular if the gradients multiply to \(-1\). For example, \(y=3x-2\) and \(y=-\frac{1}{3}x+8\) are perpendicular because \(3\times\left(-\frac{1}{3}\right)=-1\).
What is the general form of a straight line?
General form is \(ax+by+c=0\), usually with integer coefficients and \(a\) positive. The line with gradient \(\frac{2}{3}\) through \((-1,2)\) is \(2x-3y+8=0\) in general form.
What do the gradient and intercept mean in a linear model?
The gradient is the rate of change and the intercept is the starting value. In \(C=95t+140\) for a tree-lopping job, $95 is charged for each hour and $140 is a fixed fee.
Which NESA outcomes cover Straight Line Graphs?
Graphing lines from the gradient and intercept and linear models are MA5‑LIN‑C‑02. The distance, midpoint and gradient formulas, general form and parallel and perpendicular lines are MA5‑LIN‑P‑01, Path content in Stage 5 of the NSW Mathematics K–10 Syllabus (2022).