Investigating the equation of a straight line

Transcription

1 Task one What is the general form of a straight line equation? Open the Desmos app on your ipad If you do not have the app, then you can access Desmos by going to and then click on the red button that says Start Graphing. 1. Plot the following equations by typing each one fully into the input bar on the left hand side of the screen. Highlight the ones that are straight lines. Describe the shape of any that are not straight lines. y = 2x y = x 2 y = x + x 2 y + 3 = x 2y = 3x x 3 + x = y 4x + 1 = y y 2 = x Describe in words what all of the straight line equations have in common: Task two What changes the features of a straight line? y = 2x + 1 y = 4x + 1 y = x + 1 y = 0.8x + 1 y = 1 2 x + 1 Take a picture of the screen to print and stick in the space above. Answer the following questions in the space below. 2. What do these lines have in common? Page 1 of 6

2 3. Write the lines in order of steepness (least to most steep): Investigating the equation of a straight line 4. Which line would you expect to be steeper and why? y = 6x + 1 y = 3x Which line would you expect to be steeper and why? y = 3x + 1 y = 1 3 x Use Desmos to check your answers to questions 4 and 5. Were you correct? 7. What have you learnt in Task 2?... Task three What changes the features of a straight line? y = 2x + 1 y = 2x 1 y = 2x + 5 y = 2x y = 2x 0.5 Take a picture of the screen to print and stick in the space above. Answer the following questions in the space below Page 2 of 6

3 2. What do these lines have in common? 3. Where do each of the lines cross the y-axis? 4. Where would the following lines cross the y-axis? y = 2x + 3 y = 2x y = 2x 5 y = 3x Use Desmos to check your answers to question 4. Were you correct? 6. What have you learnt in Task 3? Task four What changes the features of a straight line? y = 2x + 1 y = 2x 5 y = 3 2x y = 2x y = 3 2 2x Take a picture of the screen to print and stick in the space above. Answer the following questions in the space below. 2. What do these lines have in common? 3. How do these lines differ to the ones you plotted in Task 3? Why do you think this is? Page 3 of 6

4 4. Sketch on the axes what you think the following lines will look like: y = 3x y = 1 2 x y = x Task five What makes lines be horizontal or vertical? y = 2 y = 1 y = Draw the lines on the axes here: Page 4 of 6

5 3. Describe the lines. Can you explain why they look like this (think about the coordinates on the lines) Draw what you think the following lines will look like on the axes below. y = 4 y = 0 x = 4 x = Use Desmos to check your answers to question 4. Were you correct? 6. What have you learnt in Task 5?... Task six Consolidate your learning Do not use Desmos again until you are told to check your answers! 1. Write down the equations of 4 lines that are parallel to each other and that you have not plotted today Page 5 of 6

6 2. Write down the equations of 4 lines that cross the y-axis in the same place and that you have not plotted today 3. Write down an equation of a horizontal line and an equation of a vertical line that you have not plotted today Horizontal:... Vertical: Describe in words what you think the following two lines will look like. You can include a sketch if you want. y = 2x + 3 y = 4 x 5. Check all of your answers to this task on Desmos. Make any corrections with a different coloured pen so you can learn from your mistakes. 6. Write a paragraph explaining what you have learnt about the equations of straight lines: Page 6 of 6