Drawing Straight Line Graphs (Edexcel IGCSE Maths)

Drawing Linear Graphs

Spec point — 3.3F

How do I draw a straight line from a table of values?

• You may be given a table of values with no equation

• Use the x and y values to form a point with coordinates(x, y)

  • Then plot these points

  • Use a ruler to draw a straight line through them

    • All points should lie on the line

• For example

  • The points below are (-3, 0), (-2, 2), ... etc

How do I draw a straight line using y = mx + c?

• Use the equation to create your own table of values

  • Choose points that are spread out across the axes given

• For example, plot y = 2x + 1 on axes from x = 0 to x = 10

  • Substitute in x = 0, x = 5 and x = 10 to get y coordinates

    • Then plot those points

How do I draw a straight line without using a table of values?

• Assuming the equation is in the form y = mx + c

• Start at the y-intercept **, c

• Then, for every 1 unit to the right, go up** m units

  • m is the gradient

  • If m is negative, go down

  • If m is a fraction, remember that gradient is change in y divided by change in x

    • A gradient of $\frac{a}{b}$ would be $a$ units up for every $b$ units right

• This creates a sequence of points which you can then join up

  • Be careful of counting squares if axes have different scales

    • 1 unit might not be 1 square

What if the equation is not in the form y = mx + c?

• Equations will not always be presented in the form y = mx + c

• Rearranging to y = mx + c will make plotting these graphs easier

• Consider the equation $3x+5y=30$

  • Subtract 3x from both sides

    • $5y=-3x+30$

  • Divide both sides by 5

    • $y=-\frac{3}{5}x+6$

  • It can now be seen that the gradient is $-\frac{3}{5}$ and the y-intercept is 6

• Make sure you only have 1 y on one side, rather than say, 5y

How can I plot equations in the form ax + by = c?

• Instead of rearranging, equations in the form ax + by = c, like the example above, can also be plotted by considering the x and y intercepts instead

  • Substitute in x = 0 **to find the y-intercept

  • Substitute in y = 0** to find the x-intercept

  • E.g. for $3x+5y=30$

    • When $x=0$, $5y=30$, so $y=6$
    • When $y=0$, $3x=30$, so $x=10$

  • The points (0, 6) and (10, 0) can then be plotted and joined with a straight line

Exam Hint Always plot at least 3 points (just in case one of your end points is wrong!)

Worked Example On the same set of axes, draw the graphs of $\frac{y+1}{3}=x$ and $y=-\frac{3}{5}x+3$.

Answer:

Rearrange $\frac{y+1}{3}=x$ into the form $y=mx+c$ to make it easier to plot

$\begin{gathered} \frac{y + 1}{3} & = x \\ y + 1 & = 3 x \\ y = 3 x - 1 \end{gathered}$

For $y=3x-1$, create a table of values

$x$	0	1	2
$y$	-1	2	5

Plot the points (0, -1), (1, 2) and (2, 5) Connect with a straight line

Alternatively, start at the y-intercept (0, -1) and mark the next points 3 units up for every 1 unit to the right

For $y=-\frac{3}{5}x+3$, create a table of values Because of the fraction, x= 5 is a good point to include

$x$	0	3	5
$y$	3	1.2	0

Plot the points (0, 3), (3, 1.2) and (5, 0) Connect with a straight line

Alternatively, start at the y-intercept (0, 3) and mark the next points 3 units down for every 5 units to the right