Home > Subjects > Mathematics > Level 1 > 1.4 Linear algebra (AS91029) > Subject content > Straight line graphs
- Subject: Mathematics
- AS: 91029
- Level: 1
- Credits: 3
- Internal
Mathematics 1.4 Apply linear algebra in solving problems
Straight line graphs (Graphing linear equations)
Lines in the form y = mx + c
If the equation is written in this form:
- m (the number in front of x) is the gradient of the line
- c (the number by itself) is where the graph crosses on the y-axis
- remember the sign belongs to the term directly following it.
i.e. the distance up, over the distance across
Positive slope so m is positive
Negative slope so m is negative
For more information, see Straight Lines and Slope
To draw a line written in y = mx + c form:
- The value of m is the gradient.
- Write this number as a fraction if it is a whole number by putting over 1.
- Mark a point at c on the y-axis.
- From here step out the gradient. Count up the top number and along the bottom number.
- If the gradient is negative count down.
- Join the points with a ruler.
- If the gradient is negative count down the top number.
Example of a problem in context
Jan obtains two quotes for printing booklets.
Firm A quotes: "$8 plus $4 per booklet".
Firm B quotes: "$12 plus $3 per booklet".
For how many copies will the cost be the same with both firms?
Answer
Draw a graph for each firm on the same axes. This can be done by writing an equation for both lines first.
If n is the number of booklets and C is the total cost:
- the equation for Firm A is C = 4n + 8
- the equation for Firm B is C = 3n +12.
Use the equations to draw both lines.
The point where the lines intersect (4,24) will give number of booklets that can be printed for the same cost. So the printing of 4 booklets will cost the same at both firms and the cost will be $24.
Special cases
A horizontal line has equation y = c
– the gradient is 0 and c is where the line crosses on the y-axis.
A vertical line has equation x = k
– the gradient is undefined and k is where the line crosses on the x-axis.
For more information on horizontal and vertical lines see:
Horizontal and Vertical Lines
Linear equations in other forms
To graph lines which have equations that are written in a form other than y = mx + c, for instance 2x + 3y – 6, use one of the following methods:
- gradient/intercept method (first rearrange into y = mx + c form)
- two-intercept method (put y = 0 to find x-intercept, and x = 0 to find the y-intercept)
- plotting points.
For more information on graphing lines, see:
- Revision bite: Straight line graphs
- Slope of a line
- Equations of lines
- Graphing lines
- To practise graphing straight lines see: Algebra1: Graphing Linear Equations
- Algebasics – Section 11: Linear equations (Macromedia Flash® and sound required)
- Slope slider (Java™ required)
For more information on graphing lines, see:
- Revision bite: Straight line graphs
- Slope of a line
- Equations of lines
- Graphing lines
- To practise graphing straight lines see: Algebra1: Graphing Linear Equations
- Algebasics – Section 11: Linear equations (Macromedia Flash® and sound required)
- Slope slider (Java™ required)
