Read a graphical intersection
The crossing is a common point of the two graphs. Read x first and y second, using the displayed scale
- One shared location Do not combine coordinates read from different points
- Same-sign slopes Two rising lines or two falling lines can intersect when their slopes differ
- Candidate checks When equations and a candidate point are supplied, check both rules. That is a separate substitution task
Worked example
Read the common point of the two lines. Gridlines are one unit apart
\[\text{unit gridlines}\]
- \(\displaystyle x=1.5\)Read the horizontal position
- \(\displaystyle y=2.5\)Read the vertical position of the same point
- \(\displaystyle P=(1.5,2.5)\)Write the horizontal coordinate first
Common mistakes
Swapping coordinates
✕\(\displaystyle P=(2.5,1.5)\)✓\(\displaystyle P=(1.5,2.5)\)
For the worked reading, x is 1.5 and y is 2.5. Keep axis order rather than number orderDifficulty levels
introRead a positive integer crossing pair
standardRead an integer pair or horizontal coordinate, including negative values
challengeRead exact half-unit crossing coordinates
examRecognise the crossing from four supplied pairs
Questions about this topic
Must one line rise and the other fall?+
No. Distinct slopes can meet even when both lines rise or both fall
Do all pairs of lines have one intersection?+
No. Distinct parallel lines never meet, and coincident lines share every point. This practice uses two lines with different slopes
Can I use a calculator?+
No. This topic is practised without a calculator
Which year level and chapter is this?+
Year 9 Mathematics, chapter 4: Linear relations
In this chapter
Construct a table of values from a formulaRead coordinates and points from a straight-line graph4A Points, tables and linear relations: Decide whether a point lies on a lineFind the axis intercepts of a line4C Horizontal, vertical and through-origin lines: Recognise horizontal, vertical and through-origin graphsClassify and compare gradients from graphsFind the gradient of a line through two points4E Direct proportion: Use a direct-proportion model4E Direct proportion: Read and interpret direct-proportion graphsRead the vertical-axis intercept and gradient from an equation4F Gradient-intercept form: Recognise a line or find points for its graphConstruct a line on a coordinate gridFind the equation of a line from its graph or from its intercept and slopeRecover an intercept or recognise a line from a gradient and pointFind the equation of a line through two pointsMidpoint, endpoint and distance of a coordinate segmentForm an equation of a parallel or perpendicular lineDetermine a perpendicular bisector (optional extension)4J Linear modelling: Construct a linear model from a descriptionInterpret the graph of a linear model4K Graphical simultaneous equations: Check a candidate point against two lines (optional extension)Read the point of intersection of two lines (optional extension)