Unit 6

The equation of a straight line is y=mx+c 

y being the y value in a set of coordinates

m being the gradient 

x being the x value in a set of coordinates

c being the y intercept (where the line crosses the y axis)

for example :

y=4x + 5 

4 would be the gradient (m)

5 would be the y intercept (c)

Midpoint can be found two ways :

Using 2 points or using the graph

Graph : use the graph to draw a line between the 2 points. draw a right angled triangle to join up the points with the line as the hypotenuse, Half each length of the traingle and mark the point.

2 points : E.G. find the midpoint of these points (2,4) (6,8) 

Add the two x coordinates and half it ( 2+6 = 8 8/2=4)

Add the two y coordinates and half it (4+8=12 12/2=6)

Put them beside each other in coordinate form : (4,6)

Using the coordinates (5,8) (4,6)

• First find the gradient using the formula (y2-y1) / (x2-x1)    (6-8) / (4-5) = -2 / -1 = 2
• Put the gradient into the equation of a straight line  : y=2x + c
• To find 'C', the y intercept, substitute the points into the formula :

8=(4*5) + C

8 = 20 + C

C = 8-20 = -12

• So the equation is y=2x - 12

Two perpendicular lines' gradient always multiply to -1. You could also call it the negative reciprocal.

In a question about forming perpendicular lines, they will always give you the point of where the perpendicular lines cross. This means you can work out the equation of the perpendicular line.

For example : find the perpendicular line to y=3x + 5 going through (5,4)

As the gradient is 3x, the gradient of the perpendicular line is the negative reciprocal : -3

So the equation of the perpendicular line is y=-3 + C

To work out C, substitute the point where they cross into the equation :

4 = (-3 * 5) + C

C= 4--15 = 19

So the equation of the line is y=-3x + 19