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Read coordinates and points from a straight-line graph

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Line L rises across a coordinate grid with horizontal values from zero to six and vertical values from negative two to six. Point P is marked on the line in the upper right part of the planeLP123456-2-11234560xy

What are the coordinates of the marked point?

Year 9, Chapter 4, 4 difficulty levels, No calculatorBuild a worksheet

Reading a straight-line graph

Read the labelled scales and trace to the requested line. A rule is not needed when the graph shows the values clearly. Write the horizontal value x first and the vertical value y second

\[(x,y)\]
  1. Given a horizontal value Move vertically to the line, then horizontally to the vertical scale
  2. Given a vertical value Move horizontally to the line, then vertically to the horizontal scale
  3. Scaled axes Use the value of an interval rather than treating every interval as one
  4. Axis crossings At the horizontal-axis crossing the vertical coordinate is zero. At the vertical-axis crossing the horizontal coordinate is zero \(\displaystyle \begin{gathered}(x,0)\\(0,y)\end{gathered}\)

Common mistakes

Swapping the coordinate order
✕\(\displaystyle P=(3,5)\)✓\(\displaystyle P=(5,3)\)
For a point with horizontal coordinate five and vertical coordinate three, write the horizontal value first
Counting intervals as units
✕\(\displaystyle y=4\)✓\(\displaystyle y=4\times20=80\)
Four intervals above zero represent eighty when each interval is worth twenty
Dropping a negative sign
✕\(\displaystyle x=3\)✓\(\displaystyle x=-3\)
A point three units left of the origin has a negative horizontal coordinate

Difficulty levels

introRead a single line in both coordinate directions
standardRead the named line when two lines are shown
challengeRead scaled axes and positions halfway between gridlines
examChoose a point on the named line

Questions about this topic

Which coordinate comes first?+

Write the horizontal coordinate first, then the vertical coordinate

What if the two axes use different scales?+

Read each axis separately. A horizontal interval and a vertical interval need not represent the same amount

Do I need to find a rule first?+

No. Trace directly to the named line and read the other coordinate from the scale

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)