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Linear Equations Graphing and Solutions

Gain proficiency in graphing linear equations and finding their solutions algebraically. Practice evaluating expressions and determining intercepts. Explore solving systems of equations graphically and checking solutions.

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Linear Equations Graphing and Solutions

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  1. 2 (-4 , 0) (0 , 3) ANSWER ANSWER Warm Up #3 1.Evaluate 5x + 2y forx = 2 andy = –4. 2.Find the x and y intercepts of the equation –3x + 4y = 12.

  2. Graph both lines on the same graph: 3x – 2y = 6 and 5x + 2y = 10 Line 1: x int. ( , 0 ) 2 y int. ( 0 , ) -3 Line 2: x int. ( , 0 ) 2 y int. ( 0 , ) 5 Recall Graphing from Standard Form

  3. Begin by graphing both equations, as shown at the right. From the graph, the lines appear to intersect at (3, –4). You can check this algebraically as follows. EXAMPLE 1 Solve a system graphically Graph the linear system and estimate the solution. Then check the solution algebraically. 4x + y = 8 (2 , 0) (0 , 8) Equation 1 2x – 3y = 18 (9 , 0) (0 , -6) Equation 2 SOLUTION

  4. 4(3) +(–4) 8 8 = 8 2(3) – 3(– 4) 18 6 + 12 18 12 –4 8 18 = 18 ? ? ? ? = = = = EXAMPLE 1 Solve a system graphically Equation 2 Equation 1 4x+ y= 8 2x– 3y= 18 The solution is (3, –4).

  5. GET THE WHITEBOARDS 

  6. Graph both lines on the same graph: y = -2x + 4 and y = 3x - 2 They Intersect Estimate ( 1.2 , 1.8 )

  7. Check (1.2 , 1.8) y = -2x + 4 and y = 3x - 2 1.8 = -2(1.2)+ 4 and 1.8 = 3(1.2) - 2 1.8 = -2.4 + 4 and 1.8 = 3.6 - 2 1.8 = 1.6 and 1.8 = 1.6 Not exact, but close. Many times when estimating from a graph you can only get an approximation.

  8. Graph both lines on the same graph: 3x – 2y = 6 and 5x + 2y = 10 Line 1: x int. ( , 0 ) 2 y int. ( 0 , ) -3 Line 2: x int. ( , 0 ) 2 y int. ( 0 , ) 5 They intersect at the point ( 2 , 0 )

  9. Graph this system of linear equations, then Give the solution: y = 1/5 x + 2 y = -5/3 x + 5

  10. Graph this system of linear equations, then Give the solution : y = 2x - 1 y = 2x + 2

  11. Graph this system of linear equations, then Give the solution : y = 1/3 x + 2 -x + 3y = 6 Add x and divide by 3 y = 1/3 x + 2

  12. Classwork Assignment WS 3.1 (1-11 odd and 17-20)

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