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Straight Line Graphs

Int 2. Straight Line Graphs. Drawing Straight line graphs. The gradient. The gradient from coordinates. www.mathsrevision.com. The y intercept y = mx + c. Other forms / rearranging equation. Int 2. Q1. A house is valued at £50 000.

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Straight Line Graphs

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  1. Int 2 Straight Line Graphs Drawing Straight line graphs The gradient The gradient from coordinates www.mathsrevision.com The y intercept y = mx + c Other forms / rearranging equation Created by Mr.Lafferty Maths Dept

  2. Int 2 Q1. A house is valued at £50 000. Calculate its value after 4 years, if it appreciates by 5% each year. Starter Questions Q2. Calculate 3.36 x 70 to 2 significant figures. www.mathsrevision.com Q3. Calculate the volume of a cylinder with radius 5cm and height 100 cm. Created by Mr.Lafferty Maths Dept

  3. Int 2 Straight Line Graphs Learning Intention Success Criteria • To draw graphs by using a coordinate table • Understand the key points of drawing a straight line graph • Be able to plot a straight line graph www.mathsrevision.com Created by Mr.Lafferty Maths Dept

  4. y 10 9 8 7 6 5 4 3 2 1 x 0 -10 1 2 3 4 5 6 7 9 10 -9 -8 -6 -4 -3 -2 8 -7 -5 -1 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 Drawing Straight Line Graphs y = mx + c y = x x y 0 3 -4 y = 3x+1 0 3 -4 x y 2 -2 0 -5 1 7 y = 2x y = x - 3 x y x y 8 0 4 0 3 -4 -3 1 5 0 6 -8 Created by Mr. Lafferty Maths Dept

  5. Int 2 Straight Line Graphs • Key Points • Make a table • Calculate and plot 3 coordinates • 3. Draw a line through points www.mathsrevision.com Created by Mr.Lafferty Maths Dept

  6. Straight Line Graphs Int 2 Now try Exercise 1 Odd numbers MIA (page 33) www.mathsrevision.com Created by Mr.Lafferty Maths Dept

  7. Int 2 Starter Questions Q1. Write this number in full to 1 sig. figs Q2. Calculate the volume of the triangular prism. 20cm www.mathsrevision.com 12cm 8cm Created by Mr.Lafferty Maths Dept

  8. Int 2 The Gradient of a Line Learning Intention Success Criteria • To explain how to calculate the gradient using right angled triangles • Gradient is : • change in vertical height divided by • change in horizontal distance www.mathsrevision.com • 2. Calculate simple gradients. Created by Mr.Lafferty Maths Dept

  9. Change in vertical height Change in horizontal distance Difference in y -coordinates Int 2 The Gradient The gradient is the measure of steepness of a line www.mathsrevision.com Difference in x -coordinates The steeper a line the bigger the gradient Created by Mr.Lafferty Maths Dept

  10. Int 2 m = V = H 3 The Gradient 4 3 m = V = H 2 www.mathsrevision.com 3 m = V = H 5 2 m = V = H 6 Created by Mr.Lafferty Maths Dept

  11. The Gradient Int 2 Round the class Exercise 2 MIA (page 36) www.mathsrevision.com Created by Mr.Lafferty Maths Dept

  12. Int 2 The Gradient of a Line Learning Intention Success Criteria • To explain positive and negative gradients using coordinates. • Know gradient formula. • 2. Calculate gradients given two coordinates. www.mathsrevision.com Created by Mr.Lafferty Maths Dept

  13. The gradient using coordinates Int 2 m = gradient y-axis m = Y2 – Y1 X2 – X1 y2 www.mathsrevision.com y1 x-axis O x1 x2 www.mathsrevision.com

  14. The gradient using coordinates Int 2 Find the gradient of the line. m = gradient y-axis m = Y2 – Y1 X2 – X1 m = 10 – 4 5 – 2 www.mathsrevision.com m = 6 = 2 3 x-axis O www.mathsrevision.com

  15. The gradient using coordinates Int 2 Find the gradient of the two lines. y-axis m = Y2 – Y1 X2 – X1 m = Y2 – Y1 X2 – X1 m = 8 - 2 3 - 1 m = 8 – 2 -3 – (-1) m = 6 = -3 -2 m = 6 = 3 2 x-axis O www.mathsrevision.com

  16. The gradient using coordinates Int 2 The gradient formula is : (y2 – y1) (x2 – x1) Gradient = m = www.mathsrevision.com It is a measure of how steep a line is A line sloping up from left to right is a positive gradient A line sloping down from left to right is a negative gradient Created by Mr.Lafferty Maths Dept

  17. The gradient using coordinates Int 2 Exercise 3 Q1 – Q3 MIA (page 37) www.mathsrevision.com Created by Mr.Lafferty Maths Dept

  18. Int 2 Starter Questions Q1. Write out in full to 2 sig. figs. Q2. A superstore make 20% profit on each can of soup they sell. If they buy in a can for 50p. What is the selling price. www.mathsrevision.com Q3. A hemisphere has a diameter of 10cm. Calculate its volume. Created by Mr.Lafferty Maths Dept

  19. Int 2 The Gradient of a Line Learning Intention Success Criteria • To explain the connection between the straight line equation and the gradient. • Understand the term standard form. • 2. Identify the gradient m from the standard form. www.mathsrevision.com Created by Mr.Lafferty Maths Dept

  20. y 10 9 8 7 6 5 4 3 2 1 x 0 -10 1 2 3 4 5 6 7 9 10 -9 -8 -6 -4 -3 -2 8 -7 -5 -1 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 Straight line equation and the gradient connection y = -x - 5 y = 2x + 1 x y 3 0 1 x y 0 1 3 -5 -6 -8 1 3 7 m = -1 m = 2 Created by Mr. Lafferty Maths Dept

  21. Straight Line Equation S4 Credit All straight lines have the equation of the form y = mx + c Let’s investigate properties www.mathsrevision.com (You need GeoGebra to run link) Created by Mr.Lafferty Maths Dept

  22. Straight Line Equation y 10 All straight lines have the equation of the form lines are parallel if they have the same gradient 9 8 y = mx + c 7 6 5 4 3 www.mathsrevision.com Where line meets y-axis 2 Gradient 1 x 0 10 1 2 3 4 5 6 7 8 9 Find the equations of the following lines y = -0.5x+2 y = x y = x+4 y = 4x+2 Created by Mr.Lafferty Maths Dept

  23. The Gradient of a Line Int 2 Now try Exercise 3 Q4 – Q9 MIA (page 38) www.mathsrevision.com Created by Mr.Lafferty Maths Dept

  24. Int 2 Starter Questions Q1. Write out in full to 1 significant fig. Q2. A computer store buys in a laptop for £500. They want to make a 40% profit. How much do they sell it for. www.mathsrevision.com Q3. A line is parallel to y = 2x. Write down its equation Created by Mr.Lafferty Maths Dept

  25. lines are parallel if same gradient Straight Line Equation All straight lines have the equation of the form Slope left to right upwards positive gradient y = mx + c www.mathsrevision.com y - intercept Gradient y intercept is were line cuts y axis Slope left to right downwards negative gradient Created by Mr.Lafferty Maths Dept

  26. Straight Line Graphs Int 2 Now try Exercise 4 MIA (page 41 ) www.mathsrevision.com Created by Mr.Lafferty Maths Dept

  27. Int 2 Starter Questions Q1. The points ( 1, 4) and (3, 11) lie on a line. Find the gradient of the line. Q2. Complete the table given : y = 3x+1 www.mathsrevision.com Q3. Are the two lines parallel. Explain answer y = x + 2 and y = 2x + 2 Created by Mr.Lafferty Maths Dept

  28. Int 2 Straight Line Equation Learning Intention Success Criteria • To show how to rearrange straight line equations into standard form and then identify the gradient and the • y - intercept. • Be able to rearrange straight line equations. • y = mx + c www.mathsrevision.com • Identify the gradient m and y – intercept c from the standard form. • y = mx + c Created by Mr.Lafferty Maths Dept

  29. This is called the standard form Straight Line Equation All straight lines have an equation of the form y = mx + c Where line meets y-axis Gradient www.mathsrevision.com If two lines have the same gradient they are parallel. y = 2x y = 2x+4 Created by Mr.Lafferty Maths Dept

  30. Just a bit of algebra Straight Line Equation Rearrange the following straight line equations into standard form and identify the gradient and y-intercept. Standard form m c y – 3x = 4 y = 3x + 4 3 4 www.mathsrevision.com 2y – 2x = 6 y = x + 3 1 3 y – x + 5 = 0 y = x - 5 1 -5 4y – 8 = 0 y = 2 0 2 Created by Mr.Lafferty Maths Dept

  31. Straight Line Equation Find the a line parallel to y – x = 0 and passing through (0,3). Standard form m c x – y = 0 y = x 1 0 www.mathsrevision.com A line parallel to y = x has same gradient therefore m = 1 Since it passes through (0,3) then c = 3 Using standard form line is y = x + 3 Created by Mr.Lafferty Maths Dept

  32. Straight Line Equation Int 2 Now try Ex 5 MIA (page 45) www.mathsrevision.com Created by Mr.Lafferty Maths Dept

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