Straight Lines Learning Outcomes  Revise representing a function by an arrow diagram, using the terms domain and range and notation f(x) = x+1 for x → x +1  Make tables of linear functions in order to draw their graphs.  Be able to deduce the significance of ‘m’ and ‘c’ in y = mx + c Deduce the product of the gradients of two perpendicular lines is -1  Given a series of linear graphs and equations be able to match the correct equation with the graph  Be able to derive a linear relationship from a straight line graph  Use straight line graphs in practical situations

Straight Lines Representing a function by and arrow diagram A straight line is always of the form y = m x +c where m = the gradient of the line c = the y axis intercept A straight line can be thought of as a function machine. For example if y = m x +c we can represent this with the function machine x 3+ 1 IN OUT xy

Straight Lines Make a table of values -3 ≤ x ≤ 2 for: a) y = 2 x – 4b) y = -2 x – 3 c) 2 y = 3 x – 4 x x2x - 4 y x x - 3 y y = -2 x – 3 y = 2 x –

Straight Lines c) 2y = 3x – 4 x /2x3/2x - 2 y y = 3 / 2 x – 2 Must be in the form y = m x + c

Straight Lines Finding the gradient Consider the points A (x 1,y 1 ) and B(x 2,y 2 ) x y B(x 2,y 2 ) A(x 1,y 1 ) change in x x 2 – x 1 change in y y 2 – y 1 gradient = change in y value change in x value m = y 2 – y 1 x 2 – x 1

Straight Lines Finding the gradient Examples Find the gradient of the line joining a) (3, 6) and (8, 16) b) (-4, 5) and (4, -11) (3, 6) (8, 16) (-4, 5) (4, -11) a) b)

Straight Lines Perpendicular and Parallel Lines m1m1 m2m2 If two lines are perpendicular the product of the gradient is -1 m 1 x m 2 = -1 Write down the gradients of the lines perpendicular to: a) y =3x + 4b) y = 4x – 5c) 2y = 3x +4d) 2y = -5x – 2

Straight Lines Perpendicular and Parallel Lines Write down the gradient and intercept for each of the following lines, then draw a sketch for each. a) y =3x – 4 b) 3y = 5x – 2b) 3x + y + 4= 0

Straight Lines Additional Notes

Straight Lines  Revise representing a function by an arrow diagram, using the terms domain and range and notation f(x) = x+1 for x → x +1  Make tables of linear functions in order to draw their graphs.  Be able to deduce the significance of ‘m’ and ‘c’ in y = mx + c Deduce the product of the gradients of two perpendicular lines is -1  Given a series of linear graphs and equations be able to match the correct equation with the graph  Be able to derive a linear relationship from a straight line graph  Use straight line graphs in practical situations Can Revise Do Further       Learning Outcomes: At the end of the topic I will be able to     