Drawing Straight Line Graphs

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Drawing Straight Line Graphs Revision

Drawing Straight Line Graphs

When asked to draw a straight line, there are 2 methods you can use, but it’s good to know both.

  • Using a table/list of x, y coordinate values the line passes through, or
  • Using the equation of the line, in the form y = mx + c.

Make sure you are familiar with the following topics before continuing:

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Method 1: Table of Values Method

The table of values method involves calculating values of y for different values of x.

Example: Draw a graph for the  line y = 2x - 3.

Step 1: Construct a table with suitable x values

drawing straight line graphs table of values method

Step 2: Find the values of y for each x value.

To work out the missing values, we use the equation like a formula, substituting the values from the table in, we get the following:

When x = -2, we get y = (2\times-2) - 3 = -7

When x = 0, we get y = (2\times0) - 3 = -3

When x = 2, we get y = (2\times2) - 3 = 1

When x = 4, we get y = (2\times4) - 3 = 5

drawing straight line graphs table of values method

Step 3: So, we know that the line passes through

(-2, -7), (0, -3), (2, 1) and (4, 5)

Now all that remains is to plot them on a pair of axes and draw a straight line through them. The result should look like the graph below.

drawing straight line graphs table of values method plot
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using y=mx+c to draw straight line graphs

Method 2: Using y=mx+c

You can use y=mx+c to plot a straight line graph.

Example: Plot the straight-line graph with equation 3y + 9x = 12.

using y=mx+c to draw straight line graphs

Rearranging this equation to be in the form y = mx +c, by subtracting 9x from each side

 

3y = -9x + 12

 

Then, divide both sides by 3, to get it in the form y=mx+c:

 

y = -3x + 4

 

So, the y-intercept is 4, and the gradient is -3 – so each time x increases by 1, y decreases by 3

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Drawing Straight Line Graphs Example Questions

To find the missing value, substitute the given values into the equation.

 

When x = -1, we get y = \dfrac{1}{2} \times (-1) + 5 = 4.5

 

When x = 2, we get y = \dfrac{1}{2} \times (2) + 5 = 6

 

When y = 7, we get 7 = \dfrac{1}{2}x + 5

 

Subtract 5 from both sides of this equation to get

 

2 = \dfrac{1}{2}x

 

Multiplying both sides by 2, we immediately get x = 4. The completed table looks like:

drawing straight line graphs example 1 answer table

 

Plotting these points and using them to draw the graph should look like:

drawing straight line graphs example 1 answer graph

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Let’s rearrange this equation. Subtract 1 from both sides:

 

2y = 8x - 1

 

Then, divide both sides by 2:

 

y = 4x - \dfrac{1}{2}

 

So, the y-intercept is -\frac{1}{2}, and the gradient is 4 – so each time x increases by 1, y increases by 4.

 

This is enough information to draw the graph. The result should look like the figure below.

drawing straight line graphs example 2 answer

 

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Rearranging this equation to be in the form y = mx +c, by adding 0.5 to both sides,

 

y = -0.5x + 0.5

 

So, the y-intercept is \dfrac{1}{2}, and the gradient is -\dfrac{1}{2} – so each time x increases by 1, y decreases by 0.5

 

The result should look like the figure below.

drawing straight line graphs example 2 answer

 

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We can rearrange this equation by subtracting 2 from both sides:

 

2y = 3x - 2

 

Then, dividing both sides by 2:

y = \dfrac{3}{2}x - 1

 

So, the y-intercept is -1, and the gradient is \dfrac{3}{2} – so each time x increases by 1, y increases by 1.5

 

The result should look like the figure below.

drawing straight line graphs example 4 answer

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We can rearrange this equation by subtracting 4x \text{ and } 2  from both sides:

 

y = -4x - 2

 

So, the y-intercept is -2, and the gradient is -4 – so each time x increases by 1, y decreases by 4

 

The result should look like the figure below.

drawing straight line graphs example 5 answer

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Drawing Straight Line Graphs Worksheet and Example Questions

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Drawing Straight Line Graphs Drill Questions

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