Equation from a graph
Read the intercept, calculate the gradient and place both in the equation
\[y=mx+c\]
- Intercept Read the vertical coordinate at the vertical-axis crossing \(\displaystyle (0,c)\)
- Gradient Use signed coordinate changes in the same direction \(\displaystyle m=\frac{y_2-y_1}{x_2-x_1}\)
- Notation The order of the terms may change without changing their roles \(\displaystyle mx+c=c+mx\)
- Check Substitute another visible point into the completed equation
Common mistakes
Swapping the coefficients
✕\(\displaystyle y=-5x+\frac{3}{2}\)✓\(\displaystyle y=\frac{3}{2}x-5\)
The gradient is three halves and the intercept is negative five. The gradient multiplies the variable; the intercept is the constantInverting the changes
✕\(\displaystyle m=\frac{6}{9}\)✓\(\displaystyle m=\frac{9}{6}\)
The vertical change is 9 and the horizontal change is 6. The vertical change belongs in the numeratorDifficulty levels
introRecognise a rule from a stated gradient and intercept
standardComplete the gradient and intercept in a supplied form from a graph, including horizontal lines
challengeComplete the coefficients using exact third and quarter gradients and a visible intercept
examRecognise a complete equation from a graph without intermediate prompts
Questions about this topic
Is the left edge the vertical axis?+
Only when the horizontal coordinate there is zero. Use the scale, not the frame
What if the intercept is outside the picture?+
Use two points to find the gradient, then substitute a point to recover the intercept. The later two-point topic combines those steps
Can the gradient be zero?+
Yes. A horizontal line has the same vertical coordinate at every point
Can I use a calculator?+
A calculator is allowed unless a question is marked no 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)