The Straight Line

  A straight line is the shortest distance between
two points.

 

The Gradient of a line is a measure of its slope relative to the x axis.

A positive gradient goes upwards, from left to right.

 

 

A negative gradient goes downwards, from left to right.

 

 

Gradient

The gradient is found by dividing the vertical distance by
the horizontal distance.

Example

The horizontal is 2 units. The vertical is 4 units.

The gradient is 2

 

Gradient Triangle

This can be used to find a vertical, horizontal or gradient

Examples

Find gradient given vertical and horizontal

 

 

 

Find horizontal given vertical and gradient

Find vertical given horizontal and gradient

Gradient formula

 

Drawing A line from its equation

To draw a line from its equation

• Draw a table with the letters x and y.
• Pick numbers for x and put them in the table.
• To calculate y, take a value for x and substitute into the given equation.
• Plot the points (x,y)

 

Example

 

This gives the points

(0,0) , (1,2) , (2,4), (3,6) and (4,8)

Plotting these points and joining with a straight lines gives

Extrapolating the table backwards

 

       The line y = x has values

and graph

 

Harder lines

• Draw a table with the letters x and y.
• Pick numbers for x and put them in the table.
• To calculate y, take a value for x and multiply it by the number in front of it in the given equation. Now add or subtract the whole number in the given equation.
• Fill in your value for y
• Plot the points (x,y)

Example

 

 

The equation of a straight line

           y = mx + c
Where m= gradient and c = y-intercept,
the value of y when x is zero.

Example

 

Plotting the  graph of  a line from its equation.

Finding the equation of  a line from its graph.

Straight Line - Part 2