Drawing Straight Line Graphs

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:

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.

 

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.

 

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.

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.