# Drawing Straight Line Graphs

## 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:

**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

**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

**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.

**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.

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

## Drawing Straight Line Graphs Example Questions

**Question 1:** Below is a table of coordinates of the line y = \dfrac{1}{2}x + 5. Complete the table, then plot the points and the straight-line.

**[2 marks]**

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:

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

**Question 2:** Plot the graph of the equation 2y + 1 = 8x

**[2 marks]**

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.

**Question 3:** Plot the graph of the equation y - \dfrac{1}{2} = -\dfrac{1}{2}x

**[2 marks]**

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.

**Question 4:** Plot the graph of the equation 2y + 2 = 3x

**[2 marks]**

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.

**Question 5:** Plot the graph of the equation y + 4x +2= 0

**[2 marks]**

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.