Example 1: Set up a table of values (with x-values between 3 and 3) and use it to draw the graph of 3. Press MENU 2: VIEW A: SHOW TABLE 1. Select the GRAPHS option: Or Press MENU 5: TRACE 1: GRAPH TRACE Then press the x-value you would like to see 2. Write the equation in the bottom script where f(x)= is and press ENTER 4. From these values you can draw the graph manually making sure you label your axis and relevant co-ordinate points Page 1 of 5
Example 2: Use your CAS to draw graphs for the following sets of x- and y-values. Find the rule relating y and x in each case. 4. Scroll down to the bottom of the screen where it 1. Select LISTS & SPREADSHEETS from the home 5. Scroll to the left of the screen where is says click 2. Label your column A x and label your column B HINT: Make sure after you have entered all the values that the bold selected cell is not an entry cell. I.e. press enter after your final entry 6. Press MENU 4: ANALYSE 6: REGRESSION 3. Press CTRL i 5: ADD DATA & STATISTICS 7. The calculator now shows you the equation to the line. (y = 1x + 4). HINT: from this you can also identify the gradient (m = 1) and the y-intercept (c = 4). Page 2 of 5
Example 3: Find the gradient of the following straight line. Follow steps in example 2: 1. Select LISTS & SPREADSHEETS from the home 2. Label your column A x and label your column B 7. The calculator now shows you the equation to the line. (y = 1.43x + 1.57). HINT: from this you can also identify the gradient (m = 1.43) and the y-intercept (c = 1.57). 8. To do another question the same as this example you do not have to start again. Press CTRL LEFT to go back to page 1.1 and change your two co-ordinate points. Eg. Changing points to (Ex 4.3 Q2) (1, 3) and (5, 7). 3. Press CTRL i 5: ADD DATA & STATISTICS 4. Scroll down to the bottom of the screen where it 9. Press CTRL RIGHT to go to page 1.2. your graph will now be changed showing the new equation. 5. Scroll to the left of the screen where is says click 6. Press MENU 4: ANALYSE 6: REGRESSION (y = 1x + 2) gradient: m = 1 and y-intercept: c = 2 Exercise 4.4: Equations of a straight line Page 3 of 5
Example 4: Find the equation of the straight line that has a gradient of 2 and passes through the point (1, 5) 8. The calculator now shows you the equation to the line. (y = 2x + 3). HINT: from this you can also identify the gradient (m = 2) and the y-intercept (c = 3). 1. First find a second co-ordinate point using your gradient and the given co-ordinate point. Gradient of 2 means y will move up two units and x will move to the right one unit. (1 + 1, 5 + 2) = (2, 7) The new co-ordinate point is (2,7) Using the two co-ordinate points (1,5) (2,7) use the CAS to draw a graph and find the equation. 2. Select LISTS & SPREADSHEETS from the home 3. Label your column A x and label your column B 4. Press CTRL i 5: ADD DATA & STATISTICS 5. Scroll down to the bottom of the screen where it 6. Scroll to the left of the screen where is says click 7. Press MENU 4: ANALYSE 6: REGRESSION Page 4 of 5
Example 5: Find the y-intercept and gradient and, hence, sketch the graph of 2x + 5y = 8 1. First rearrange the equation in the form of y = mx + c From the home menu, select calculator. HINT: make sure you have no predefined values. Gradient: m= Y-intercept: c = (0, ) 4. Find the second co-ordinate point using your gradient and the given co-ordinate point. Gradient of means y will move down two units and x will move to the right five units. 2. Press MENU 3: ALGEBRA 1: SOLVE In the brackets write your equation, press comma, then y, close your bracket and hit enter. (0 + 5, - 2) = (5, ) The new co-ordinate point is (5, ) Using the two co-ordinate points (0, ) (5, ) use the CAS to draw a graph and find the equation. 5. Select LISTS & SPREADSHEETS from the home 6. Label your column A x and label your column B 3. Press MENU 2: NUMBER 7: FRACTION TOOLS 1: PROPER FRACTIONS, hit the up arrow until your answer in the previous line is highlighted and press ENTER twice 7. Press CTRL i 5: ADD DATA & STATISTICS 8. Scroll down to the bottom of the screen where it 9. Scroll to the left of the screen where is says click 10. Press MENU 4: ANALYSE 6: REGRESSION 11. The calculator now shows you the equation to the line. (y = -0.4x +1.6). HINT: from this you can also identify the gradient (m = -0.4) and the y-intercept (c = 1.6). Page 5 of 5