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Starter: Plot the following graphs y = 5x – 3 y = 2 y = -2x + 1 x = -3

Use the table function on the calculator to obtain co-ordinates to plot for the following equation: y = ⅓x + 3. Starter: Plot the following graphs y = 5x – 3 y = 2 y = -2x + 1 x = -3 y = ¼x + 3 y = - x + 1. Note 2: Finding Linear Equations from Graphs.

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Starter: Plot the following graphs y = 5x – 3 y = 2 y = -2x + 1 x = -3

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  1. Use the table function on the calculator to obtain co-ordinates to plot for the following equation: y = ⅓x + 3

  2. Starter:Plot the following graphs y = 5x – 3y = 2 y = -2x + 1x = -3 y = ¼x +3 y = -x + 1

  3. Note 2: Finding Linear Equations from Graphs To find the equation of a line, use the general form of a linear equation: y = mx + c y-intercept gradient

  4. Example – find the equation of this line 2  3  Locate two points on cross-gridlines These are the corners of a triangle Find the lengths of the two sides (rise is 3 and run is 2) Write the fraction RISE/RUN. If the line leans LEFT, then negative

  5. C = 1 Find the y-intercept, Use your values of m and c to write the equation y = mx + c becomes

  6. Graphics Calculator instructions • Use the stats function to find equations. • Stats Function • Delete any data in columns: (F6) DELA (F4), YES (F1) • Enter co-ordinates: (X – List 1, Y – List 2) • SET (F6): Graph type Scatter • X List List 1 • Y List List 2 EXIT • Graph points: GPH1 • Draw line: CALC (F1), X (F2) - Linear line, aX + b (F1)

  7. Now try to find the equations of these graphs

  8. m is positive as it leans to the right m = 2/2 = 1 c = – 2 y = 1x – 2 or y = x – 2 (ans)

  9. m is negative as it leans to the left m = - 4/2 = –2 c = 3 y = – 2x + 3 (ans) 

  10. m is positive as it leans to the right m = 2/6 = 1/3 c = -3 y = 1/3 x – 3 (ans) 

  11. m is negative as it leans to the left m = - 2/3 c = 1 y = – 2/3 x + 1 (ans) Note that we could have also drawn our triangle here or here Remember that, regardless of how you’ve drawn your triangle, the ratio RISE : RUN in this question will always be 4:6 or 2:3 i.e. m = 2/3

  12. m is positive as it leans to the right m = 3/4 c = 0 y = ¾ x No c NOTE If it goes through the origin then the y intercept = 0, so there will be no “c” on the end of the equation!

  13. m is negative as it leans to the left m = - 5/5 = –1 c = 0 y = – x AGAIN it goes through the origin, so y intercept is zero and there won’t be a “c”

  14. Drawing the graph using the gradient and y-intercept Example – Plot the line y = 2x – 3 using gradient and y-intercept STEP 1 Plot the y-intercept, – 3 STEP 2 Write the gradient as a fraction Y = 2x - 3 The rise is 2 The run is 1 And it leans to the RIGHT (+)  STEP 3 Beginning at the y-intercept,– 3, make a triangle whose horizontal is 1 and vertical is 2. Plot a point.  STEP 4 Now we have 2 points! Join this new point to the y-intercept. Arrows on ends and label line

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