Intro to Linear Equations Algebra 6 - AGMath.com

1 AlgebraIntro to Linear Equations :72 xy521 xy1232 yxLinear Equations generally contain two variables: x and a Linear equation,y is called the dependent variable andx is the independent is because y is dependent on what you plug-in for domain of a Linear equation is the set of all x-coordinates and therange is the set of all :State the range and the domain for each set of points (-3, -3) (-1, 1) (1, 5) (3, 9) (5, 13)2. (-5, 8) (-2, 5) (1, 5) (4, 9) (7, 13)Practice:State the range and domain for each set of points graphed below as aninequality:Ex. #1 Domain -4 < x < 4 Range: 5 < y < 912345 AlgebraIntro to Linear a domain, it is easy to find the range for any Linear :Find the range for the given domain:1. 32 xy {D: -3, -2, -1, 0}2. 32 xy {D: 6, 1, -4, -9}Practice:Find the range for the given domain:1. 73 xy{D: -3, -2, -1, 0}2.

2 132 xy{D: 6, 3, 0, -3, -6}3. 1062 xy{D: -1, 1, 3, 5}In problems like #3 above, it helps a lot to solve for y before plugging invalues for the :Find the range for the given domain. Begin by solving for 5472 xy{D: -3, -2, -1, 0}2. xy963 {D: 6, 3, 0, -3}3. 1035 xy{D: x>5 }AlgebraIntro to Linear EquationsName_____ Period each graph below, state the domain and range using an inequality:1. Domain: _____ Range: _____2. Domain: _____ Range: _____3. Domain: _____ Range: _____4. Domain: _____ Range: _____1234 List the Domain and Range for each set of points listed below:5. (9,1) (8,2) (7, 3) (6, 4) (5, 5)5. Domain: _____ Range: _____6. (-3, -3) (-3, -4) (-3, -5) (-3, -6)6. Domain: _____ Range: _____7. 3 xy for x = -3, -4, 5, and 67. Domain: _____ Range: _____8. 52 xy for x > 38. Domain: {D: x > 3}____ Range: _____AlgebraIntro to Linear EquationsName_____ Period each domain below, find the range for each equation.

3 Solve for y where 32 xy {D: -1, 0, 1, 2}9. Range: _____10. 521 xy {D: -4, -2, 0, 2}10. Range: _____11. 1263 xy {D: -5, -3, 1, 5}11. Range: _____12. 4 yx {D: 4, 1, -1, -9}12. Range: _____13. 63 xy {D: -3, 0, 3, 9}13. Range: _____14. 1035 xy {D: -15, -10, -5, 0}14. Range: _____15. 732 xyx {D: -4, 4, 12, 20}15. Range: _____AlgebraGraphing A Linear graph a Linear Equation:1. Solve for Setup a table of x and y Plot at least three coordinates and connect xyGraph232 xyPracticePlot each of the following Equations on the same 43 xy2. 543 xy3. 93 xyAlgebraGraphing A Linear each of the following Equations on the same 5 yx2. 923 xy3. xy2123 PracticePlot each of the following Equations on the same 53 yx2. yx 433. )3(325 xyAlgebraGraphing Linear EquationsName_____ Period _____Graph each equation below on the graphs 9 xy2.

4 1223 xy3. 426 yx4. )6(213 Linear EquationsName_____ Period _____Graph each equation below on the graphs 13114 xy6. xyx 3627. yx243 8. 5 Form of a Linear equation:62 yx2173 yx162 yxExamples above are Linear Equations written in Standard is Standard Form. MEMORIZE 1. No absolute value, exponents, square roots, 1 or 2 variables (A and B cannot both be zero).3. All Linear Equations can be written in Standard A, B, and C are Integers (not fractions). A should be :Label the values for A, B, and C in each Linear equation 62 yx2. 2173 yx3. 7 xExamples:Convert each equation below into Standard Form if both variables ON THE SAME SIDE OF THE 53 xy2. 433221 xy3. yx53 Practice:Convert each equation below into Standard Form if xy 52. xy4153 3. yxx )1(AlgebraStandard FormName_____ Period each equation below into Standard to remove all fractional 3 yx2.

5 Xy273 3. yx 474. yx1022 5. 7 x6. 122 y7. yx4 8. xy25 9. 34132 yx10. 25121 yx11. 73261 yx12. yx8143 AlgebraStandard FormName_____ Period Equation below is written in Standard each for y, create a table of values, and graph 3 yx14. 1236 yx15. 63 yx16. 62 yxAlgebraStandard Form and a graph, the x-intercept is where the line crosses the y-intercept is where a line crosses the :Look at the graphs below and give the coordinates ofthe x and _____y-int. _____y-int. _____y-int. _____notes:The x-intercept always occurs where y equals y-intercepts always occurs where x equals y=0 to find the x=0 to find the : Find the x and y-intercepts of will call this the coverup 123 yx2. 452 yx3. 832 yxPractice: Find the x and y-intercepts of 3035 yx2. 117 yx3. 73243 yx123 AlgebraStandard Form and :Each line below goes with one of the Linear Equations on the each equation with its graph by finding the 1232 yx2.

6 1053 yx3. 73 yxPractice: Graph each of the following using the intercepts:1. 1535 yx2. 82 yx3. 93 yxABCA lgebraStandard Form and the x and y-intercepts for each equation to Standard Form where 93 yx2. 1025 yxx-int.: _____x-int.: _____y-int. _____y-int. _____3. 79 yx4. 372 yxx-int.: _____x-int.: _____y-int. _____y-int. _____5. yx39 6. 523 xyx-int.: _____x-int.: _____y-int. _____y-int. _____7. 32 xy8. yx4122 x-int.: _____x-int.: _____y-int. _____y-int. _____9. xy 3210. 543 xyx-int.: _____x-int.: _____y-int. _____y-int. _____11. 59 xy12. 319221 xyx-int.: _____x-int.: _____y-int. _____y-int. _____Name_____ Period _____AlgebraStandard FormName_____ Period each equation below using the the intercepts. Intercepts are all whole 62 yx14. 1236 yx15. 63 yx16. 102 Slope of a line is its RISE over Read graphs left to right, just like Find a point on the graph of a Count how far you must go UP AND OVER to get to the next Write this as a fraction: : State the slope of each line:3232 is not always positive.

7 Working from left to right,if you go down and over, this is negative : State the slope of each line:Practice: State the slope of each do not need a graph to find the slope of a could you find the RISE given two coordinates? ex. (4, 2) and (8, 10)How could you find the RUN given two coordinates?Example:Find the slope of the line passing through (3, 5) and (7, 7).How far UP?How far OVER?notes:Given two coordinates: ),(11yx and ),(22yxSlope Formula: 1212xxyym memorize this!To find the slope you must divide the y s and the x minus y over x minus over s how you find the :Find the slope of a line passing through each given pair of points:1. (9, 4) (7, 10)2. (-2, -5) (4, 1)Practice:Find the slope of a line passing through each given pair of all slopes and LEAVE IMPROPER FRACTIONS:1. (-3, 0) (1, 2)2. (3, 4) (4, -1)3. (6, -2) (7, -7)4.

8 (1, -5) (-9, 1)5. (8, 4) (-5, 15)6. (-1, -5) (4, -10)AlgebraSlope-Intercept a Linear Equation:Method 1: x/y ChartMethod 2: Intercepts (from Standard Form)Use one of the methods above to graph each of the following , list the slope and the y-intercept of each xyslope: _____y-int: _____332 xyslope: _____y-int: _____Guess what form we are going to learn FormMEMORIZE THIS:bmxy Where m is the slope and b is the is the most useful form of a Linear equation, especially for : Graph each using Slope-Intercept 532 xy2. 52 xy3. 1253 xyPractice: Convert each into Slope-Intercept Form, then 217 yx2. 303 yx3. 255 yx(Why is Standard Form less useful for graphing these Equations ?)Practice: Write an equation for each line graphed belowin Slope-Intercept : Convert these answers to Standard 254 xy2. 631 xy3.

9 332 xy123 AlgebraSlope-Intercept Each into Slope-Intercept Form1. 93 yx2. 1025 yxslope: _____slope: _____y-int. _____y-int. _____3. 189 yx4. 2172 yxslope: _____slope: _____y-int. _____y-int. _____5. yx39 6. 1523 xyslope: _____slope: _____y-int. _____y-int. _____7. 3025 xy8. yx4122 slope: _____slope: _____y-int. _____y-int. _____9. xy 3210. 643 xyslope: _____slope: _____y-int. _____y-int. _____11. 59 xy12. 319221 xyslope: _____slope: _____y-int. _____y-int. _____Name_____ Period _____AlgebraSlope-Intercept FormName_____ Period each equation below using slope-intercept 532 xy14. 1835 yx15. 62 yx16. 64321 yxAlgebraQuiz :100. 532 xy200. 1835 yx300. )3,1(and )13,5(400. )5,2( and )4,3( 500. 24395 yx600. xxy 3)3(7 Intercepts:100. 632 yx200. 1545 yx300. 783 xy400. 54321 yx500. xyyx5)(2 600. 7211321 yxAlgebraQuiz Form:100.

10 Xy 3200. 143 xy300. 23121 xy400. )5(543 xy500. 31512 yx600. 232 yxStandard Form:100. 5 xy200. 521 xy300. xy523 400. 352 yx500. 10352 yx600. )(72)(21yxyx AlgebraPractice Quiz: Linear EquationsName_____ Period Each to Standard Form and list values for A, B, and 6 xy1. A=____B=____C=____2. xy72 2. A=____B=____C=____3. yx 52213. A=____B=____C=____4. y412 4. A=____B=____C=____5. 23 yx5. A=____B=____C=____State the y-intercept of each equation below:6. 4 yx6. y-int. _____7. 341 xy7. y-int. _____8. yx213 8. y-int. _____9. 352 yx9. y-int. _____10. yx 510. y-int. _____AlgebraName_____ Period _____Practice Quiz: Linear an equation in slope-intercept form for each:11. _____12. _____13. _____14. _____15. _____State the slope for each equation or pair of points:16. 1052 yx16. m=_____17. xy 3217. m=_____18. )10,9( and )5,1( 18.