Remember graphs are read from left to right like a book The Gradient. The gradient (m) of a straight line is defined to be: Remember graphs are read from left to right like a book Change in horizontal distance h Change in vertical height v

Find the gradients of the straight lines below: 3 (1) (2) 4 4 7 m = 4 7 4 m = 3 (3) 4 4 4 m = 4 m = 1

3 6 (5) (6) 8 9 8 4 9 m = = m = = 3 6 3 3

Negative Gradient Consider the straight lines shown below: (d) (e) (a) Positive gradient Lines (a) (c) and (d) slope upwards from left to right. Negative gradient Lines (b) and (e) slope downwards from left to right.

Calculate the gradients of the lines below: (1) (2) - 4 - 8 5 6

The Equation of a Straight Line. To find the equation of any straight line we require to know two things: (a) The gradient of the line. m = gradient (b) The y axis intercept of the line. c = y axis intercept The equation of a straight line is : y = m x + c Examples. Give the gradient and the y axis intercept for each of the following lines. (1) y = 6x + 5 (2) y = -4x + 2 (3) y = x - 3 m = 6 c = 5 m = -4 c = 2 m = 1 c = - 3

Finding The Equation. Find the equation of the straight lines below: x y (1) x y (2) What is the gradient ? m = 1 What is the y axis intercept? c = 2 c = 1 Now use y = m x + c y = x + 2

m = -2 (3) x y x y (4) c = 3 • y = -2x + 3 • • • c = -2

x y (5) (6) x y • c = 2 • • • c = 6

Straight Line Equation All straight lines have an equation of the form y = mx + c Gradient Where line meets y-axis Two special cases: Horizontal lines have equation y = a constant Vertical lines have equation x = a constant

Straight Line- Special cases Horizontal lines have equations y = a constant Vertical lines have equation x = a constant y x y x x = -1 x = 4 x = -5 y = 5 y = 2 y = -1 Gradient = 0 Gradient undefined