Drawing straight line graphs
Select Lesson
Exam Board
Select an option
Statistics
Sets and Venn diagrams
Sampling and bias
Collecting data: types and classes of data
Mean, median, mode and range
Simple charts and graphs
Pie charts
Scatter graphs
Frequency tables: finding averages
Grouped frequency tables
Box plots - Higher
Cumulative frequency - Higher
Histograms and frequency density - Higher
Interpreting data
Comparing data sets
Probability
Trigonometry
Angles and geometry
Shapes and area
Properties of 2D shapes
Congruence: conditions for congruent triangles
Similar shapes: Scaling
The four transformations
Area and perimeter: Formulae
Area and circumference of circles: Formulae
3D shapes: faces, edges, vertices
Surface area of 3D shapes: Nets, formulae
Volume of 3D shapes: Formulae
Volume of 3D shapes: Comparing, rates of flow
Area and volume scale factors
Projections and elevations of 3D shapes
Ratio proportion and rates of change
Graphs
Coordinates and midpoints
Straight line graphs
Drawing straight line graphs
Finding the gradient of a straight line
Equation of a straight line: y = mx + c
Coordinates and ratio
Parallel and perpendicular lines
Quadratic graphs
Reciprocal and cubic graphs
Exponential graphs and circles - Higher
Trigonometric graphs - Higher
Solving equations using graphs
Graph transformations - Higher
Real-life graphs
Distance-time graphs
Velocity-time graphs - Higher
Gradients of real-life graphs - Higher
Algebra
Simplifying algebraic expressions
Multiplying and dividing algebraic expressions
Single brackets: Expanding and factorising
Double brackets: Expanding and factorising
Double and triple brackets - Higher
Solving equations
Expressions, equations, formulae, functions and identities
Writing formulae and equations from word problems
Writing formulae and equations from diagrams
Rearranging formulae
Factorising quadratics
The quadratic formula - Higher
Complete the square - Higher
Algebraic fractions - Higher
Sequences
Finding the nth term
Solving inequalities
Inequalities on graphs - Higher
Iteration - Higher
Simultaneous equations: elimination and substitution
Non-linear simultaneous equations - Higher
Algebraic proof - Higher
Composite and inverse functions - Higher
Number
Types of numbers
Order of operations: BODMAS
Multiplying and dividing by powers of 10
Multiplying and dividing whole numbers
Multiplying and dividing decimals
Negative numbers: add, subtract, multiply, divide
Prime numbers and prime factorisation
Multiples, factors and prime factors
LCM and HCF
Fractions
Fractions, decimals and percentages
Writing recurring decimals as fractions
Rounding: Integers, decimal places, significant figures
Estimation
Error intervals
Upper and lower bounds - Higher
Powers and roots: Square and cube numbers
Laws of indices: multiply, divide, brackets
Index laws: negative and fractional indices - Higher
Surds: Simplify, add and subtract - Higher
Rationalising surds - Higher
Standard form calculations
Explainer Video
Summary
Drawing straight line graphs
In a nutshell
There are three types of straight lines: diagonal, horizontal and vertical. Generally, straight lines can be described using two quantities: the gradient and the -intercept. The exception is vertical lines which are solely defined by their -intercept.
Equations of the straight line graphs
The general equation of a straight line is
where is the gradient of the line and is the -intercept. If is not zero, then the line is diagonal. If is zero, then the line is horizontal:
A vertical line does not have this equation. Instead it has equation
where is the -intercept.
Using the equation to draw the line
One way to draw a straight line graph is to find two points that the line passes through, before joining up those points and extending the line beyond them. Follow this procedure to draw a diagonal line:
PROCEDURE
| 1. | Start with the -intercept, given by , since this is on the -axis. Hence you have that the point is on the line. Mark this on the coordinate grid. |
| 2. | Pick an -value (other than zero, since this will just give you the point you already have) and insert it into the equation of the line to find the corresponding -coordinate. Mark on this second point. |
| 3. | Join it up the two points and extend the line beyond them. |
For horizontal lines () or vertical lines () it is much more straightforward. The value of or gives the -intercept and -intercept respectively, so whichever type of line you have, draw that straight line through that intercept.
Example 1
A line has equation . Find the coordinates of any two points on the line and hence draw the line given by the equation.
Firstly, use the -intercept to find the first point: . Hence when , .
Point 1:
Next, pick a non-zero -value. For example, . Insert this into the equation of the line:
So when , .
Point 2:
Plot the two points found ( and ) then join them up, extending beyond those points.
Using a table and plotting points
An alternative to the method outlined above is to use a table of points and to plot them. Joining up the points gives the line. Doing this requires being able to insert one coordinate into the equation of the line to identify the corresponding coordinate.
procedure
| 1. | Take the value of a coordinate given in the table and insert it into the equation of the line. |
| 2. | Add the corresponding coordinate found from the equation to the table. |
| 3. | Mark the point given by the corresponding coordinates to the graph. |
| 4. | Do this for all of the entries in the table. |
| 5. | Join up the points marked to give the line. |
Example 2
Consider the table below, which gives a some of the coordinates on the line
| | | | | | |
| | | | | | |
Complete the table, plot the points on a graph and hence draw the line .
The first missing value is the -coordinate when . Hence insert this -value into the equation of the line:
So the corresponding -coordinate is and thus the point is on the line.
Repeating this procedure for the other missing values ( and ) gives the following complete table:
| | | | | | |
| | | | | | |
The points you have are , , , and . Plotting these and connecting them looks like this:
FAQs - Frequently Asked Questions
How do you use a table of coordinates to draw a straight line graph?
Insert one coordinate into the equation of the line to identify the corresponding coordinate. Complete the table and plot the points, then join them up into a line.
How do you draw a straight line graph?
One way to draw a straight line graph is to find two points that the line passes through, before joining up those points and extending the line beyond them.
What are the equations of straight lines?
The general equation of a (diagonal or horizontal) straight line is y=mx+c where m and c are constants. A vertical line instead has equation x=d where d is a constant.