Gradient

• The Gradient of a straight line shows how steep a straight line is.

• Gradient = 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑖𝑛 𝑦−𝑐𝑜𝑟𝑑𝑖𝑛𝑎𝑡𝑒𝑠

𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑖𝑛 𝑥−𝑐𝑜𝑜𝑟𝑑𝑖𝑛𝑎𝑡𝑒

𝑚 =𝑦2 − 𝑦1

𝑥2 − 𝑥1

Examples

The Gradient of this line = 3

3= 1

Gradient = 4

2= 2

The line is steeper, and so the Gradient is larger

The form y=mx+c

When the equation of a straight line is written in the form y=mx+c, the gradient of the line m and the intercept on the y-axis is c.

Slope or gradient (how steep the line is)

Y intercept (where the line across the y axis)

Finding the equation of line

(-3,-6) (0,4)

m = −4 −(−6)

0 −(−3)=

2

3

𝑚 =𝑦2 − 𝑦1

𝑥2 − 𝑥1

𝑦 = 𝑚𝑥 + 𝑐