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Straight line graphs

Straight line graphs. A revision guide. Write down the co-ordinates of A, B, C and D :. (3,4). A. (-3,2). D. B. (1,-2). (-5,-3). C. True or false?. Straight line equations can contain terms. A True B False C Don’t know. Which one is the general equation of a straight line?. A

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Straight line graphs

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  1. Straight line graphs A revision guide

  2. Write down the co-ordinates of A, B, C and D : (3,4) A (-3,2) D B (1,-2) (-5,-3) C

  3. True or false? Straight line equations can contain terms. A True B False C Don’t know

  4. Which one is the general equation of a straight line? A B C

  5. What does m represent in the equation of a straight line? A the intercept B the gradient C the first coordinate

  6. A where the line hits the y-axis B the steepness of the line C where the line hits the x-axis

  7. What does c represent in the equation of a straight line? A the y-intercept B the gradient C the first coordinate

  8. A where the line hits the y-axis B the steepness of the line C where the line hits the x-axis

  9. What is the gradient of the line? A The gradient is y B The gradient is 2 C The gradient is 4

  10. What is the y-intercept of the line? A The y-intercept is -6 B The y-intercept is 2 C The y-intercept is -3

  11. The equation of the line with gradient = 1 and y-intercept = 5 is: A B C

  12. The equation of the line with a gradient = -1 and y-intercept = -4 is: A B C

  13. The equation of the line with a gradient = 2 and y-intercept = -4 is: A B C

  14. Summary 1 • Co-ordinates are written as (x,y) • The general equation of a straight line is • m is the gradient which describes the steepness of the line, the larger m is the steeper the line is! • c is the y-intercept, it is the point at which the line hits the y-axis • To identify the gradient and y-intercept of an equation, we must compare the equation to • If the equation is NOT in the form then we must re-arrange the equation to get it in this form

  15. What is the value of the y-intercept? A -1 B 10 C 2

  16. A line with a positive gradient goes up towards the POSITIVE QUADRANT Which of these graphs has a negative gradient? A Both graphs B Neither graph C Graph A D Graph B

  17. Which line has the largest Gradient? A B Steepness If it were a SLIDE which one would scare you most ? C

  18. Parallel lines have the same WHAT? • y-intercept • Gradient • x-intercept

  19. If you are given two co-ordinates, you can find the gradient of a straight line using the ‘formula’ Where , and , are co-ordinates on the line!

  20. Using find the gradient of a line with co-ordinates (2,9) and (0,7)

  21. Using find the gradient of a line with co-ordinates (3,3) and (-5,7)

  22. Using find the gradient of a line with co-ordinates (-5,3) and (-4,9)

  23. Find any two co-ordinates which lie on the line with equation

  24. Are the points (0,-3) and (1,2) on the line with equation ?

  25. Exercise 1: Write down the gradient and y-intercept of the lines with the following equations 3

  26. Exercise 2: Write down the equation of the line with the following gradients and y-intercepts a) m = 2 , c = 4 b) m = -1 , c = -2 c) m = 1 , c =

  27. Exercise 3: Using find the gradient of the line with co-ordinates • (2,4) and (4,3) • (3,-5) and (5,5) • (-3,-1) and (-4,2) x1 , y1 x2 , y2 x2 , y2 x1 , y1 x2 , y2 x1 , y1

  28. Exercise 4: Do these points lie on the line ? • (3,1) x , y Equation is in BALANCE SO THE POINT (3,1) LIES ON THE LINE!!!

  29. Exercise 4: Do these points lie on the line ? • (2,4) x , y Equation is NOTin BALANCE SO THE POINT (2,4) is NOT ON THE LINE!!!

  30. Exercise 4: Do these points lie on the line ? • (0,-5) x , y Equation is NOTin BALANCE SO THE POINT (0,-5) is NOT ON THE LINE!!!

  31. Exercise 5: Find any two co-ordinates on the following line ? When When

  32. Exercise 6: Which of the following graphs are parallel?

  33. Plotting a Graph: 0 1 2 3 4 For the line when when when

  34. Plotting Line Graphs 0 1 2 3 4 (-2, 0) (-1, 1) (0, 2) (1, 3) (2, 4) Now we have some co-ordinates, so we just plot them to draw the line 

  35. y y = x + 2 5 X 4 X 3 X 2 0 1 3 2 4 X 1 (-1, 1) (-2, 0) (1, 3) (2, 4) (0, 2) X X 1 0 -5 -4 -3 -2 -1 2 4 5 3 -1 -2 -3 -4 -5

  36. 4 3 2 1 -5 -4 -3 -2 -1 0 1 2 3 4 5 -1 -2 -3 -4 -5 HORIZONTAL & VERTICAL LINES y (x,y) (3,4) (3,1) x y = -2 (0,-2) (2,-2) (-4,-2) (3,-5) x = 3

  37. 4 3 2 1 -5 -4 -3 -2 -1 0 1 2 3 4 5 -1 -2 -3 -4 -5 HORIZONTAL & VERTICAL LINES y (x,y) (-2,4) y = 2 (-4,2) (0,2) (2,2) (-2,1) x (-2,-5) x = -2

  38. (x,y) HORIZONTAL & VERTICAL LINES y x = 1 x = 5 4 x = -4 3 2 y = 1 1 1 x -5 -4 -3 -2 -1 0 1 2 3 4 5 -1 -2 -3 y = -4 4 -4 -5 5 2 3

  39. TASK 1 A) Plot the straight line graph with equation • Take values of from -2 to 2 • 2cm ≡ 1 unit for the y-axis • 4cm ≡ 1 unit for the x-axis B) Write down the co-ordinate of the y-intercept C) Draw the line on the same axes D) Write down the co-ordinate of their point of intersection

  40. TASK 2 A) Plot the straight line graph with equation • Take values of from -3 to 3 • Use an appropriate scale B) Write down the co-ordinate of the y-intercept C) From the graph find the y when C) Draw the line on the same axes D) Write down the co-ordinate of the point of intersection of the two lines

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