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# Linear Functions

### Graphing and Writing Linear Functions

Problem | Solution |
---|---|

Graph g(x)=2x +1 Compare this graph to the graph of f(x)=2x | 1. Choose 3 values for x & plug them into the equation 2x +1. Now you have an x and y value for three ordered pairs. 2. Plot the 3 ordered pairs on the graph. 3. Plug in the same 3 x values for g(x)=2x+1.Graph and compare. |

Graph the linear functions f(x)=-3x and g(x)= -3x-6. | 1.Choose 4 values for x & plug them into the equation f(x)=-3x. Now you have and x and y value for four ordered pairs. 2. Plot the 4 ordered pairs on the graph. 3. Use the same 4 x values for g(x)=-3x-6. 4. Plot the 4 ordered pair values/Compare. |

Find the equation of the line with slope -3 and y-intercept (0,-5). Write the equation using function notation. | 1. Knowns-slope-(m=-3), y-intercept (b=-5) 2. Use slope intercept form y=mx +b and plug in values y=-3(x) +(-5)or y=-3x-5. 3. In function notation y is replace with f(x), so f(x)=-3x-5. |

Find the equation of the line through the points (4,0) and (-4,-5). Write the equation using function notation. | 1. Find slope of the line using slope formula m=y2-y1/x2-x1 2. m=-5-0/-4-4....m=-5/-8=5/8. Slope 5/8 3. Use point slope form y-y1= m(x-x1)... y-0=5/8(x-4). 8y=5x-20 4.Solve for y. y=5/8x- 20/8 or y=5/8x-5/2 5.Substitute f(x) for y. |

Find the equation of the horizontal line containing the point (2,3). Write the equation using function notation. | 1. A horizontal line's equation is y=c. 2. Because the line contains the ordered pair (2,3), the equation is y=3. 3. To write in function notation replace the y with f(x).....so f(x)=3. |

Find the equation of the line containing the point (4,4) and parallel to the line 2x +3y=-6. Then write the equation in standard form. | 1 Parallel lines will have equal slopes. 2. Find the slope of 2x + 3y=-6, by using the slope-intercept form y=mx + b... y=-2/3x-2. 3.A parallel line to this line (slope -2/3)will also have slope -2/3. Use point-slope form y-y1=m(x-x1)/Solve/2x+3y=20 |

Write a function that describes the line containing a point (4,4) and perpendicular to the line 2x +3y=-6 | 1. A line that is perpendicular to another line will have (-) reciprocal of slope of that line. 2. Use point-slope equation y-y1=m(x-x1). 3. Plug in values x1=4,y1=4,m=3/2 (reciprocal of 2/3). Solve. 4. Change y to f(x) for function notation. |

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