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1 Topic 4.2.2 Graphing A x + B y = C

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2 California Standards: 6.0 Students graph a linear equation and compute the x - and y -intercepts (e.g., graph 2 x + 6 y = 4). They are also able to sketch the region defined by linear inequality (e.g., they sketch the region defined by 2 x + 6 y < 4). 7.0 Students verify that a point lies on a line, given an equation of the line. Students are able to derive linear equations by using the point- slope formula. What it means for you: You’ll learn how to graph a straight line by joining two points. Key Words: linear equation Topic 4.2.2

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3 y = 2 x (2, 4) (–2, –4) Graphing A x + B y = C Every point on a line is a solution to the equation of the line. If you know any two solutions (any two coordinate pairs), then you can join the points with a straight line. Topic 4.2.2 If you know any two solutions (any two coordinate pairs)…

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4 Graphing A x + B y = C Graphing the Line A x + B y = C Using Two Points The graph of the equation A x + B y = C consists of all points ( x, y ) whose coordinates satisfy A x + B y = C. To graph the line, you just need to plot two points on it and join them together with a straight line. Topic 4.2.2

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5 Graphing A x + B y = C Rearrange the equation so it is in the form y = P x + Q. Choose two values of x and substitute them into your equation to find the corresponding values of y. Topic 4.2.2 Plot the two points and draw a straight line through them. Plot a third point to check that the line is correct — the point should lie on the line. Here’s how you go about it:

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6 Graphing A x + B y = C Example 1 Plot and label the graph of the equation x – y = –3. Solution follows… Topic 4.2.2 Rearrange the equation to get y = x + 3. Solution Choose two values of x, then draw a table to help you find the y -values: (4, 7) y = x + 3, so y = 4 + 3 = 74 (–2, 1) y = x + 3, so y = –2 + 3 = 1–2 ( x, y ) yx Solution continues…

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7 Plot and label the graph of the equation x – y = –3. Graphing A x + B y = C Example 1 When you plot the graph, the line should be straight. Solution (continued) Topic 4.2.2 When x = 1 Check your solution: So ( x, y ) = (1, 4) y = x + 3 = 1 + 3 = 4 (1, 4) lies on the line — which means the line is correct. (1, 4) (4, 7) (–2, 1) ( x, y )

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8 Graphing A x + B y = C Example 2 Plot and label the graph of the equation y = –2 x – 4. Solution follows… Topic 4.2.2 Solution Choose two values of x, then draw a table to help you find the y -values: (2, –8) y = –2 x – 4 = –2(2) – 4 = –82 (–2, 0) y = –2 x – 4 = –2(–2) – 4 = 0–2 ( x, y ) yx Solution continues…

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9 (0, –4) Plot and label the graph of the equation y = –2 x – 4. Graphing A x + B y = C Example 2 Use the points in the table to plot the graph. Solution (continued) Topic 4.2.2 x = 0 Check: (0, –4) lies on the line — which means the line is correct. (2, –8) (–2, 0) ( x, y ) y = –2 x – 4 = –2(0) – 4 = 0 – 4 = – 4

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10 Graphing A x + B y = C Guided Practice Solution follows… 1. (–1, –3) and (3, 5) 2. (–3, 4) and (4, –3) Graph the line through the two points in each of Exercises 1–2. Topic 4.2.2 (–1, –3) (3, 5) (–3, 4) (4, –3) 21

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11 Graph and label the lines of the equations in Exercises 3–4. Graphing A x + B y = C Guided Practice Solution follows… 3. – x – 2 y = 4 4. 2 x – 3 y = 6 Topic 4.2.2 4 2 x – 3 y = 6 – x – 2 y = 4 3

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12 Graph and label the lines of the equations in Exercises 5–6. Graphing A x + B y = C Guided Practice Solution follows… 5. 5 y – 3 x = 15 6. 7 y – 2 x = –14 Topic 4.2.2 5 5 y – 3 x = 15 6 7 y – 2 x = –14

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13 Independent Practice Solution follows… In Exercises 1–4, graph the line through each set of points. Graphing A x + B y = C Topic 4.2.2 1. (–1, –2) and (2, 4) 2. (–1, –1) and (1, 3) 3. (0, 0) and (2, 6) 4. (0, –2) and (1, 1) (2, 4) (–1, –2) 1 (1, 3) (–1, –1) 2 3 (2, 6) (0, 0) 4 (1, 1) (0, –2)

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14 Independent Practice Solution follows… Graph and label the lines of the equations in Exercises 5–8. Graphing A x + B y = C Topic 4.2.2 5. x + y = 8 6. y – x = 10 7. 2 x + y = –3 8. 5 x + y = –12 5 x + y = 8 6 y – x = 10 7 2 x + y = –3 8 5 x + y = –12

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15 Independent Practice Solution follows… Graphing A x + B y = C Topic 4.2.2 9. –3 x + y = –6 10. –10 x + y = 21 11. 2 x – y = –14 12. 6 x + 2 y = 18 Graph and label the lines of the equations in Exercises 9–12. 9 –3 x + y = –6 10 –10 x + y = 21 11 2 x – y = –14 12 6 x + 2 y = 18

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16 Independent Practice Solution follows… Graphing A x + B y = C Topic 4.2.2 13. 8 x + 4 y = 24 14. 12 x – 4 y = 8 15. 3 x – 9 y = –27 16. 2 x – 8 y = 16 Graph and label the lines of the equations in Exercises 13–16. 13 8 x + 4 y = 24 14 12 x – 4 y = 8 15 3 x – 9 y = –27 16 2 x – 8 y = 16

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17 Round Up It’s easy to make a mistake when working out y -values, so choose x -values that will make the algebra easy (for example, 0 and 1). And it’s always a good idea to check your line by plotting a third point. Graphing A x + B y = C Topic 4.2.2

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