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Graphing Ax + By = C Topic 4.2.2

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**Graphing Ax + By = C 4.2.2 Topic California Standards:**

6.0 Students graph a linear equation and compute the x- and y-intercepts (e.g., graph 2x + 6y = 4). They are also able to sketch the region defined by linear inequality (e.g., they sketch the region defined by 2x + 6y < 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

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**Graphing Ax + By = C 4.2.2 Topic**

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

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**Graphing Ax + By = C 4.2.2 Topic**

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

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**Graphing Ax + By = C 4.2.2 Topic Here’s how you go about it:**

• Rearrange the equation so it is in the form y = Px + Q. • Choose two values of x and substitute them into your equation to find the corresponding values of y. • 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.

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**Graphing Ax + By = C 4.2.2 Topic**

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

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**Graphing Ax + By = C 4.2.2 Topic**

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

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**Graphing Ax + By = C 4.2.2 Topic**

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

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**Graphing Ax + By = C 4.2.2 Topic**

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

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**Graphing Ax + By = C 4.2.2 Topic Guided Practice**

Graph the line through the two points in each of Exercises 1–2. 2 1 (–1, –3) and (3, 5) (–3, 4) and (4, –3) (–1, –3) (3, 5) (–3, 4) (4, –3) Solution follows…

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**Graphing Ax + By = C 4.2.2 Topic Guided Practice**

Graph and label the lines of the equations in Exercises 3–4. –x – 2y = 4 2x – 3y = 6 4 2x – 3y = 6 –x – 2y = 4 3 Solution follows…

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**Graphing Ax + By = C 4.2.2 Topic Guided Practice**

Graph and label the lines of the equations in Exercises 5–6. 5y – 3x = 15 7y – 2x = –14 5 5y – 3x = 15 6 7y – 2x = –14 Solution follows…

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**Graphing Ax + By = C 4.2.2 Topic Independent Practice**

In Exercises 1–4, graph the line through each set of points. (–1, –2) and (2, 4) (–1, –1) and (1, 3) (0, 0) and (2, 6) (0, –2) and (1, 1) 2 1 3 4 (2, 6) (2, 4) (1, 3) (1, 1) (0, 0) (–1, –1) (–1, –2) (0, –2) Solution follows…

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**Graphing Ax + By = C 4.2.2 Topic Independent Practice**

Graph and label the lines of the equations in Exercises 5–8. x + y = 8 y – x = 10 2x + y = –3 5x + y = –12 7 2x + y = –3 6 y – x = 10 8 5x + y = –12 5 x + y = 8 Solution follows…

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**Graphing Ax + By = C 4.2.2 Topic Independent Practice**

Graph and label the lines of the equations in Exercises 9–12. –3x + y = –6 –10x + y = 21 2x – y = –14 6x + 2y = 18 9 –3x + y = –6 10 –10x + y = 21 11 2x – y = –14 12 6x + 2y = 18 Solution follows…

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**Graphing Ax + By = C 4.2.2 Topic Independent Practice**

Graph and label the lines of the equations in Exercises 13–16. 8x + 4y = 24 12x – 4y = 8 3x – 9y = –27 2x – 8y = 16 14 12x – 4y = 8 13 8x + 4y = 24 15 3x – 9y = –27 16 2x – 8y = 16 Solution follows…

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**Graphing Ax + By = C 4.2.2 Topic 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.

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