1. Coordinates and Linear Equations Miss Hudson’s Maths

2. E (1, -2) A (4, 2) B (0, 2) C (-3, 1) D (-1, 0) 2 1 12 -2 1 st quadrant2 nd quadrant 3 rd quadrant4 th quadrant The point (0,0) is called the origin Plotting Points Remember: Across ( ) and then up/down ( ) Miss Hudson’s Maths

3. Drawing Straight Line Graphs eg 1: y = x + 2 x y -2 0 1 2 3 0 1 2 3 4 5..... Method A: Rostering 5 4 3 2 1 -2 -3 -3 -2 -1 0 1 2 3 Miss Hudson’s Maths

4. Gradient (Slope) The gradient tells us how steep a line is. The gradient of line AB = The gradient of line BC = 2 3 rise run 4 Miss Hudson’s Maths

5. A line sloping this way: has a positive gradient A line sloping this way: has a negative gradient Two special cases: A horizontal line has gradient = 0 rise = 0 A vertical line has gradient = undefined run = 0 gradient = = 0 gradient = we can’t divide by zero Miss Hudson’s Maths

6. Drawing Straight Line Graphs eg 1: Draw the line y = x y 1.Mark 2 on the y-axis 2.Step off the gradient a couple of times x 1 3 1 3 3. Draw the line - long y-intercept = gradient = 2 Method B: Gradient – Intercept Method -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 4 3 2 1 -2 -3 The general equation for a straight line is y = mx + c where m is the gradient and c is the y-intercept. Miss Hudson’s Maths

7. eg 2: Draw the line y = -2x + 1 x y 1.Mark 1 on the y axis 2.Step off the gradient a couple of times x 1 -2 y-intercept = gradient = 1 -2 1 3. Draw the line - long Remember the gradient is -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 4 3 2 1 -2 -3 -4 Miss Hudson’s Maths

8. Horizontal & Vertical Lines A horizontal line has an equation of the form y = a number eg y = 3 is a line parallel to the x-axis passing through 3 12 3 4 5 1 2 34 5 -2 -3 -4 -5 0 y = 3 A vertical line has an equation of the form x = a number eg x = -2 is a line parallel to the y-axis passing through -2 x = -2 Miss Hudson’s Maths

9. Remember: The general equation for a straight line is y = mx + c where m is the gradient and c is the y-intercept. The equation of this graph would be written as: y = mx + c 1 1 2 3 4 5 6 5432154321 Miss Hudson’s Maths