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Algebra I

Algebra I. Coordinate Plane, Graphing by table and intercepts. Give the coordinates of each letter. Graph the function y = 2 x – 1 with domain –2, –1, 0, 1, and 2. Then identify the range of the function. GUIDED PRACTICE. Plot the point in a coordinate plane. Describe the

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Algebra I

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  1. Algebra I Coordinate Plane, Graphing by table and intercepts

  2. Give the coordinates of each letter.

  3. Graph the function y = 2x – 1 with domain –2, –1, 0, 1, and 2. Then identify the range of the function.

  4. GUIDED PRACTICE Plot the point in a coordinate plane. Describe the location of each point. Which quadrant is it in?

  5. Graph the function y = – x + 2 with domain –6, –3, 0, 3, and 6. Then identify the range of the function. 1 3 Plot the point in a coordinate plane. Describe the location of the point.

  6. Graph y=–x–2 with domain –2, –1, 0, 1, and 2.

  7. Rewrite the equation so y is a function of x. 3x+ 4y = 16 –6x – 2y = –12

  8. (1, –4) (3, 4) A B (5, –3) (–1, –2) C D EXAMPLE 1 Which ordered pair is a solution of 3x – y = 7? Tell whether (4, -1/2) is a solution of x + 2y = 5.

  9. Graphing by tables

  10. Graph the equation –2x +y =–3.

  11. y + 3x = –2

  12. Graph (a) y = 2 and (b) x = –1.

  13. x+ 4 – Graph the functiony= with domainx 0. Then identify the range of the function. 1 2 EXAMPLE 4 SOLUTION STEP1 Make a table. Recommendation: Choose numbers that are easily divisible by 2 so that when you Multiply by ½, the value will become a “nice” number. In addition, notice that the Domain STARTS at zero.

  14. Graph the function y=–3x + 1 with domain x  0.Then identify the range of the function.

  15. Intercepts

  16. Rewriting in standard form • X and Y are on the same side • Coefficients are INTEGERS. Get rid of any fractions by multiplying by a common multiple of the denominators. • X is in the first position, Y is in the second position and X is ALWAYS nonnegative!

  17. Example • -x+y=6 • -2x+y=-4 • y=-3x-4

  18. A harder cases • Y=(3/4)x+2 • Y=(3/2)x+(1/2)

  19. EXAMPLE 1 Find the x-intercept and the y-intercept of the graph of 2x + 7y = 28. Write the x-intercept and y-intercept in coordinate form.

  20. GUIDED PRACTICE Find the x-intercept and the y-intercept of the graph of the equation. 3x + 2y = 6

  21. GUIDED PRACTICE Find the x-intercept and the y-intercept of the graph of the equation. 4x – 2y = 10

  22. EXAMPLE 2 Graph the equation x + 2y =4 using intercepts

  23. EXAMPLE 3 Use a graph to find intercepts

  24. EXAMPLE 2 GUIDED PRACTICE Graph the equation 6x + 7y = 42. Label the points where the line crosses the axes.

  25. EXAMPLE 4 Solve a multi-step problem EVENT PLANNING You are helping to plan an awards banquet for your school, and you need to rent tables to seat 180 people. Tables come in two sizes. Small tables seat 4 people, and large tables seat 6 people. This situation can be modeled by the equation 4x + 6y = 180 where xis the number of small tables and yis the number of large tables. • Find the intercepts of the graph of the equation. • Graph the equation. • Give four possibilities for the number of each size table you could rent.

  26. y-intercept 4x + 6y = 180 4x + 6y = 180  4(0) + 6y = 180 4x + 6(0) = 180 x-intercept x = 45 y = 30 EXAMPLE 4 SOLUTION STEP 1 Find the intercepts.

  27. EXAMPLE 4 STEP2 Graph the equation. The x-intercept is 45, so plot the point (45, 0).The y-intercept is 30, so plot the point (0, 30). Since x and yboth represent numbers of tables, neither xnor ycan be negative. So, instead of drawing a line, draw the part of the line that is in Quadrant I.

  28. EXAMPLE 4 STEP 3 Find the number of tables. For this problem, only whole-number values of x and y make sense. You can see that the line passes through the points (0, 30), (15, 20), (30, 10), and (45, 0).

  29. A recycling company pays $1 per used ink jet cartridge and $2 per used laser cartridge. The company paid acustomer $14. This situation is given by x + 2y = 14 wherexis the number of ink jet cartridges andythe number of laser cartridges. Use intercepts to graph the equation. Give four possibilities for the number of each type of cartridge that could have been recycled. Daily Homework Quiz

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