Starter Questions Factorise 5x + 10

The Straight Line Equation Learning Intention To explain and draw straight lines of the form y = mx + c.

The Straight Line Equation By calculating the gradient of each line, write down the equation of the line y The Straight Line Equation 1 2 4 3 5 x

The Straight Line Equation Gradient = vertical height horizontal distance = 4 1 = 4 Equation of line is y = 4x Line 2 Gradient = vertical height horizontal distance = 3 2 Equation of line is y = 3x 2 Line 3 Gradient = vertical height horizontal distance = 2 2 = 1 Equation of line is y = x

The Straight Line Equation Gradient = vertical height horizontal distance = 1 2 Equation of line is y = 1x 2 Gradient = vertical height horizontal distance = 1 4 Line 5 Equation of line is y = 1x 4

The Straight Line Equation All the lines we have previously looked at all passed through the origin at (0,0) i.e. y = 2x, y = 3x, y = ½x, y = 5x etc… Gradient = 3 Gradient = 5 Gradient = 2 Gradient = ½ What about straight lines that do not pass through the origin

The Straight Line Equation Example Draw the line of y = 2x on a suitable coordinate diagram y = 2x + 2 y x 0 1 2 3 4 Same gradient, but slightly higher up y 2 4 6 8 y = 2x On the same diagram, draw the graph of y = 2x + 2 x 0 1 2 3 4 y 2(0)+2 2(0)+2 2(0)+2 2(3)+2 2(4)+2 =2 =4 =6 =8 =10 x What do you notice about the second line?

The Straight Line Equation Example Draw the line of y = x on a suitable coordinate diagram y x y = x + 4 0 1 2 3 4 Same gradient, but slightly higher up y 1 2 3 4 y = x On the same diagram, draw the graph of y = x + 4 x 0 1 2 3 4 y 4 5 6 7 8 x What do you notice about the second line?

The Straight Line Equation y = x On your 4 quadrant diagram, Draw the lines of the given equations. The Straight Line Equation 1 2 3 4 5 6 7 8 9 10 -9 -8 -7 -6 -5 -4 -3 -2 -1 -10 x y x y 2 4 y = 3x+1 2 4 x y 1 2 1 4 7 y = x - 3 y = 2x + 3 x y 4 8 x y 1 2 -3 1 5 3 5 7

Straight Line Equation y 10 lines are parallel if they have the same gradient All straight lines have the equation of the form 9 8 y = mx + c 7 6 5 4 3 Where line meets y-axis 2 Gradient 1 x 1 2 3 4 5 6 7 8 9 10 Find the equations of the following lines y = x y = x+4 y = 4x+2 y = -0.5x+2

Straight Line Equation Now try Ex 4 Ch6 Page 73 Start at Q4