Content:
MA4-LIN-C-01
Plot and identify points on the Cartesian plane
- Plot and label points on the Cartesian plane of given coordinates, including those with coordinates that are not whole numbers
- Identify and record the coordinates of given points on the Cartesian plane, including those with coordinates that are not whole numbers
Plot linear relationships on the Cartesian plane
- Construct a geometric pattern and record the results in a table of values
- Represent a given number pattern (including decreasing patterns) using a table of values
- Describe a number pattern in words and generate an equation using algebraic symbols
- Apply an equation generated from a pattern to calculate the corresponding value for a smaller or larger number
- Recognise that a linear relationship can be represented by a number pattern, an equation (or a rule using algebraic symbols), a table of values, a set of pairs of coordinates and a line graphed on a Cartesian plane, and move flexibly between these representations
- Explain that there are an infinite number of ordered pairs that satisfy a given linear relationship by extending a line joining a set of points on the Cartesian plane
- Compare similarities and differences of multiple straight-line graphs on the same set of axes using graphing applications
- Describe linear relationships in real-life contexts and solve related problems
Solve linear equations using graphical techniques
- Recognise that each point on the graph of a linear relationship satisfies the equation of a line
- Apply graphs of linear relationships to solve a corresponding linear equation using graphing applications
- Graph 2 intersecting lines on the same set of axes and identify the point of intersection using either graphing applications or a table of values
- Verify that the point of intersection satisfies the equations of both lines
MA5-LIN-C-01
Find the midpoint and gradient of a line segment (interval) on the Cartesian plane
- 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, 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
- 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
- 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
- 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
