Linear Functions<br />
Standard:  Ax + By = C<br />Point Slope: y - y₁ = m(x-x₁)<br />Slope-Intercept: y = mx + b<br />Slope: m = π‘¦Β βˆ’π‘¦β‚π‘₯Β βˆ’π‘₯₁<br /...
Converting between Forms<br />Standard to Slope-Intercept<br />	Ax + By = C<br />By = -Ax + C<br />y = βˆ’π΄π‘₯+𝐢𝐡<br />y = βˆ’π΄π‘₯...
Graphing Linear FunctionsUsing Points<br />Use two points ( x, y) and  ( x₁, y₁)<br />Find these points on the graph<br />...
Graphing Linear FunctionsUsing points<br />To find Slope<br />Count π‘Ήπ’Šπ’”π’†π‘Ήπ’–π’ on graph<br />Β <br />Or<br />Use point-slope f...
Graph 3y – 9x = 3<br />First solve equation for y<br />3y – 9x = 3<br />3y + 9x – 9x = 3 + 9x<br />πŸπŸ‘ βˆ™ 3y = 3 + 9x βˆ™ πŸπŸ‘<b...
Graphing Linear FunctionsMaking a Table<br />Now select some values for domain<br />Plug values into y = 3x + 1<br />
Graphing Linear FunctionsMaking a Table<br />Graph ordered pairs<br />Draw line through points<br />
Graphing Linear FunctionsUsing intercepts<br />Find x-intercept of           7x + y = -4<br />Replace y with zero<br />7x ...
Graphing Linear FunctionsUsing intercepts<br />X-intercept is βˆ’πŸ’πŸ•<br />Line intersects x-axis at    ( βˆ’πŸ’πŸ•, 0)<br />Y-inter...
Find Equation of Function Using GraphsSlope-Intercept<br />Find where line intersects y-axis<br />This value is b<br />Fin...
Find Equation of Function Using GraphsPoint-Slope<br />Plug given point into         ( x₁, y₁ )<br />y – 2 = m( x – 3)<br ...
Parallel Linear Functions<br />y = πŸ‘πŸ x + 1<br />y = πŸ‘πŸ x + 4<br />Are these functions parallel?<br />Graph them<br />They...
Perpendicular Linear Functions<br />y = βˆ’πŸ‘πŸ’x + 2<br />y = πŸ’πŸ‘ x + 3<br />Are these functions perpendicular?<br />Graph them...
Parallel and Perpendicular Linear Functions<br />Parallel<br />Functions with equal slopes are parallel<br />y = mx + b<br...
TI-Nspire CAS Student Software, All TI-Nspire CAS Calculator images, September 22, 2010, Copy Righted Texas Instruments.<b...
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Linear functions

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Linear functions

  1. 1. Linear Functions<br />
  2. 2. Standard: Ax + By = C<br />Point Slope: y - y₁ = m(x-x₁)<br />Slope-Intercept: y = mx + b<br />Slope: m = π‘¦Β βˆ’π‘¦β‚π‘₯Β βˆ’π‘₯₁<br />Β <br />Linear Function Expressions and Forms<br />
  3. 3. Converting between Forms<br />Standard to Slope-Intercept<br /> Ax + By = C<br />By = -Ax + C<br />y = βˆ’π΄π‘₯+𝐢𝐡<br />y = βˆ’π΄π‘₯𝐡 + C<br />Let βˆ’π΄π΅ = m<br />Let C = b<br />y = mx + b<br />Β <br />Point-Slope to Slope<br />y - y₁ = m( x - x₁)<br />π‘¦Β βˆ’π‘¦β‚π‘₯Β βˆ’π‘₯₁ = m<br />m = π‘¦βˆ’π‘¦β‚π‘₯βˆ’π‘₯₁<br />Β <br />
  4. 4. Graphing Linear FunctionsUsing Points<br />Use two points ( x, y) and ( x₁, y₁)<br />Find these points on the graph<br />For example:<br />Let ( x, y) = ( 1, 2)<br />and ( x₁, y₁) = ( 3, 4)<br />
  5. 5. Graphing Linear FunctionsUsing points<br />To find Slope<br />Count π‘Ήπ’Šπ’”π’†π‘Ήπ’–π’ on graph<br />Β <br />Or<br />Use point-slope form<br />Y - y₁ = m( x - x₁)<br />2 - 4 = m( 1 - 3)<br />πŸΒ βˆ’πŸ’πŸΒ βˆ’πŸ‘ = m<br />m = βˆ’πŸβˆ’πŸ<br />m = 1<br />Slope is 1<br />Β <br />
  6. 6. Graph 3y – 9x = 3<br />First solve equation for y<br />3y – 9x = 3<br />3y + 9x – 9x = 3 + 9x<br />πŸπŸ‘ βˆ™ 3y = 3 + 9x βˆ™ πŸπŸ‘<br />y = 1 + 3x<br />y = 3x + 1<br />Equation is now in slope-intercept form<br />Β <br />Graphing Linear FunctionsMaking a Table<br />
  7. 7. Graphing Linear FunctionsMaking a Table<br />Now select some values for domain<br />Plug values into y = 3x + 1<br />
  8. 8. Graphing Linear FunctionsMaking a Table<br />Graph ordered pairs<br />Draw line through points<br />
  9. 9. Graphing Linear FunctionsUsing intercepts<br />Find x-intercept of 7x + y = -4<br />Replace y with zero<br />7x + 0 = -4<br />πŸπŸ• βˆ™ 7x + 0 = -4 βˆ™ πŸπŸ•<br />x = βˆ’πŸ’πŸ•<br />Β <br />Find y-intercept of 7x + y = -4<br />Replace x with zero<br />7(0) + y = -4<br />y = -4<br />
  10. 10. Graphing Linear FunctionsUsing intercepts<br />X-intercept is βˆ’πŸ’πŸ•<br />Line intersects x-axis at ( βˆ’πŸ’πŸ•, 0)<br />Y-intercept is -4<br />Line intersects y-axis at ( 0, -4)<br />Β <br />
  11. 11. Find Equation of Function Using GraphsSlope-Intercept<br />Find where line intersects y-axis<br />This value is b<br />Find slope of line by π‘Ήπ’Šπ’”π’†π‘Ήπ’–π’<br />This value is m<br />y = mx + b<br />Β <br />
  12. 12. Find Equation of Function Using GraphsPoint-Slope<br />Plug given point into ( x₁, y₁ )<br />y – 2 = m( x – 3)<br />Find slope by π‘Ήπ’Šπ’”π’†π‘Ήπ’–π’ in graph<br />Plug slope into m<br />y – 2 = 𝟏𝟐( x – 3)<br />Β <br />
  13. 13. Parallel Linear Functions<br />y = πŸ‘πŸ x + 1<br />y = πŸ‘πŸ x + 4<br />Are these functions parallel?<br />Graph them<br />They are parallel<br />Β <br />
  14. 14. Perpendicular Linear Functions<br />y = βˆ’πŸ‘πŸ’x + 2<br />y = πŸ’πŸ‘ x + 3<br />Are these functions perpendicular?<br />Graph them<br />They are Perpendicular<br />Β <br />
  15. 15. Parallel and Perpendicular Linear Functions<br />Parallel<br />Functions with equal slopes are parallel<br />y = mx + b<br />y = πŸ‘πŸ x + 1<br />y = πŸ‘πŸ x + 4<br />m = πŸ‘πŸ<br />Β <br />Perpendicular<br />Functions with reciprocal slopes are perpendicular<br />Y = mx + b<br />Y = βˆ’πŸ‘πŸ’ x + 2<br />Y = πŸ’πŸ‘ x + 3<br />M = βˆ’πŸ‘πŸ’ and m = πŸ’πŸ‘<br />Β <br />
  16. 16. TI-Nspire CAS Student Software, All TI-Nspire CAS Calculator images, September 22, 2010, Copy Righted Texas Instruments.<br />Citations<br />
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