Linear Relationships A

numberandalgebra core

Linear relationships A | NSW Curriculum Website

• MA4-LIN-C-01 determines the midpoint, gradient and length of an interval, and graphs linear relationships, with and without digital tools

📖 Prior Knowledge

Content	Prior knowledge	Used for
Ratios and Rates	- ratios	- calculating gradient
Algebraic Techniques	- substitution	- constructing tables of values from an equation
Equations	- using formulas - verifying solutions	- finding midpoint, gradient, distance - determine whether a point lies on a line
Linear Relationships	- plotting points on a Cartesian plane - $y=mx+c$	- sketching graphs - recognising equation of a straight line
Right-angled Triangles	- Pythagoras’ theorem	- calculating distance
Data Analysis	- mean	- calculating midpoint

Find the midpoint and gradient of a line segment (interval) on the Cartesian plane.pdf

• Plot and join 2 points to form an interval on the Cartesian plane and use the interval as the hypotenuse of a right-angled triangle
• Apply the relationship gradient  $m=\frac{rise}{run}$ to find the gradient/slope of the interval joining the 2 points
• Distinguish between intervals with positive and negative gradients from a diagram
• Explain why horizontal intervals have a gradient of 0 and vertical intervals have undefined gradients using the gradient relationship
• Determine the midpoint of horizontal and vertical intervals on the Cartesian plane
• Apply the process for calculating the mean to find the midpoint, $M$ of the interval joining 2 points on the Cartesian plane
• Use graphing applications to find the midpoint and gradient/slope of an interval

Find the distance between 2 points located on the Cartesian plane.pdf

• Use the interval between 2 points as the hypotenuse of a right-angled triangle on the Cartesian plane and apply Pythagoras’ theorem to determine the length of the interval joining the 2 points
• Use graphing applications to find the distance between 2 points on the Cartesian plane

Recognise and graph equations.pdf

• Recognise that equations of the form  $y=mx+c$ represent linear relationships or straight lines
• Construct tables of values and use coordinates to graph a variety of linear relationships on the Cartesian plane, with and without digital tools
• Identify the $x$- and $y$- intercepts of lines
• Determine whether a point lies on a line using substitution

Examine parallel, horizontal and vertical lines.pdf

• Explain that parallel lines have equal gradients/slopes
• Explain why the $x$-axis has the equation $y=0$ and the $y$-axis has the equation $x=0$
• Recognise $y=c$  as a line parallel to the $x$-axis and $x=k$ as a line parallel to the $y$-axis
• Graph vertical and horizontal lines