Straight Lines: Finding Equations & Drawing Graphs | Mathematics for Grade 10 PDF Download

Why do we want to know about straight lines and their equations?

• Straight Line Graphs (Linear Graphs) have lots of uses in mathematics – one use is in navigation
• We may want to know the equation of a straight line so we can program it into a computer that will plot the line on a screen, along with several others, to make shapes and graphics

How do we find the equation of a straight line?

• The general EQUATION of a straight line is y = mx + c
  • where m is the gradient
  • c is the y-axis intercept
• To find the EQUATION of a straight line you need TWO things:
  • the gradient, m
  • any point on the line
• You might find these things from a graph, another equation or two points
• You may be asked to give the equation in the form ax + by + c = 0
  (especially if m is a fraction)

Example: The line P has equation y = 4x +5.
Find the equation of the line L parallel to P which passes through the point (- 1. 3).
Give your answer in the form ax + by + c = 0 

Sketch not essential but if it doubt ...
Sketching the given line and roughly where the new line L should be will give you a good idea if your final answer is realistic or not

How do we draw the graph of a straight line from an equation?

• Before you start trying to draw a straight line, make sure you understand how to find the equation of a straight line – that will help you understand this
• How we draw a straight line depends on what form the equation is given in
• There are two main forms you might see:
  y = mx + c and ax + by = c
• Different ways of drawing the graph of a straight line:
  • From the form y = mx + c
    (you might be able to rearrange to this form easily)
    plot c on the y-axis
    go 1 across, m up (and repeat until you can draw the line)
  • From ax + by = c
    put x = 0 to find y-axis intercept
    put y = 0 to find x-axis intercept
    (You may prefer to rearrange to y = mx + c and use above method)

Tips

It might be easier just to plot ANY two points on the line (a third one as a check is not a bad idea either) or use the TABLE function on your calculator.

Example: On the axes below draw the lines y = 3x - 1 and 3x + 5y = 15

1. y = 3x - 1 First plot c, which is - Ion the y - axis
Then go across 1, m, which is 3, up - this has been done twice on the diagram Doing the second part twice gives you three points that are on the line and so you can be confident you have the right answer
2. 3x + 5y. = 15 When x = 0, 5y = 15 and so y = 3, therefore (0, 3) is on the line W hen y = 0, 3x = 15 and so x = 5, therefore (5, 0) is on the line Plot the two points (0, 3) and (5, 0) and join them up to get your line