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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 - yβ = m(x-xβ)<br />Slope-Intercept: y = mx + b<br />Slope: m = π¦Β βπ¦βπ₯Β βπ₯β<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 = βπ΄π₯+πΆπ΅<br />y = βπ΄π₯π΅ + C<br />Let βπ΄π΅ = m<br />Let C = b<br />y = mx + b<br />Β <br />Point-Slope to Slope<br />y - yβ = m( x - xβ)<br />π¦Β βπ¦βπ₯Β βπ₯β = m<br />m = π¦βπ¦βπ₯βπ₯β<br />Β <br />
4. 4. Graphing Linear FunctionsUsing Points<br />Use two points ( x, y) and ( xβ, yβ)<br />Find these points on the graph<br />For example:<br />Let ( x, y) = ( 1, 2)<br />and ( xβ, yβ) = ( 3, 4)<br />
5. 5. Graphing Linear FunctionsUsing points<br />To find Slope<br />Count πΉππππΉππ on graph<br />Β <br />Or<br />Use point-slope form<br />Y - yβ = m( x - xβ)<br />2 - 4 = m( 1 - 3)<br />πΒ βππΒ βπ = m<br />m = βπβπ<br />m = 1<br />Slope is 1<br />Β <br />
6. 6. Graph 3y β 9x = 3<br />First solve equation for y<br />3y β 9x = 3<br />3y + 9x β 9x = 3 + 9x<br />ππ β 3y = 3 + 9x β ππ<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π β 7x + 0 = -4 β ππ<br />x = βππ<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 βππ<br />Line intersects x-axis at ( βππ, 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π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 ( xβ, yβ )<br />y β 2 = m( x β 3)<br />Find slope by πΉππππΉππ in graph<br />Plug slope into m<br />y β 2 = ππ( x β 3)<br />Β <br />
13. 13. Parallel Linear Functions<br />y = ππ x + 1<br />y = ππ x + 4<br />Are these functions parallel?<br />Graph them<br />They are parallel<br />Β <br />
14. 14. Perpendicular Linear Functions<br />y = βππx + 2<br />y = ππ 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π x + 1<br />y = ππ x + 4<br />m = ππ<br />Β <br />Perpendicular<br />Functions with reciprocal slopes are perpendicular<br />Y = mx + b<br />Y = βππ x + 2<br />Y = ππ x + 3<br />M = βππ and m = ππ<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 />