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Lesson 6-3 (Part 1) Standard Form page 298

Lesson 6-3 (Part 1) Standard Form page 298. Objective: To graph equations using intercepts. Real-World Connection. We can use an equation to model a situation that involves exercise, as in example 5. DEFINITION. Standard form of a linear equation: Ax + By = C

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Lesson 6-3 (Part 1) Standard Form page 298

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  1. Lesson 6-3 (Part 1)Standard Formpage 298 Objective: To graph equations using intercepts.

  2. Real-World Connection • We can use an equation to model a situation that involves exercise, as in example 5.

  3. DEFINITION • Standard form of a linear equation: Ax + By = C where A, B, and C are real numbers and A and B are not zero. x-intercept—the x-coordinate of the point where a line crosses the x-axis y-intercept– the y-coordinate of the point where a line crosses the y-axis

  4. Find the x- and y-intercepts of 2x + 5y = 6. Step 2  To find the y-intercept, substitute 0 for x and solve for y. 2x + 5y = 6 2(0) + 5y = 6 5y = 6 y = The y-intercept is . 6 5 6 5 Standard Form ALGEBRA 1 LESSON 6-3 Step 1 To find the x-intercept, substitute 0 for y and solve for x. 2x + 5y = 6 2x + 5(0) = 6 2x = 6 x = 3 The x-intercept is 3. 6-3

  5. Example 1, page 299 Find the x and y intercept of 3x + 4y = 8.

  6. Example 1, page 299 Find the x-and y-intercepts of 4x – 9y = -12.

  7. Graphing Using Intercepts • Find the x-intercept by substituting zeros for y. • Find the y-intercept by substituting zeros for x. • Plot the intercepts. • Draw the line.

  8. Graph 3x + 5y = 15 using intercepts. Step 2  Plot (5, 0) and (0, 3). Draw a line through the points. Standard Form ALGEBRA 1 LESSON 6-3 Step 1  Find the intercepts. 3x + 5y = 15 3x + 5(0) = 15 Substitute 0 for y. 3x = 15 Solve for x. x = 5 3x + 5y = 15 3(0) + 5y = 15 Substitute 0 for x. 5y = 15 Solve for y. y = 3 6-3

  9. y 5 x -5 5 -5 Example 2, page 299 • Graph 2x + 3y = 12 using the x- and y-intercepts.

  10. y 5 x -5 5 -5 Example 2, page 299 • Graph 5x + 2y = -10 using the x- and y-intercepts.

  11. Special Lines In standard form Ax + By = C either A or B = 0, but not both. • If A = 0, the line is horizontal and the equation looks like: y = #. • If B = 0, the line is vertical and the equation looks like: x = #.

  12. Standard Form ALGEBRA 1 LESSON 6-3 a. Graph y = 4 b. Graph x = –3. 0 • x + 1 • y = 4 Write in standard form. For all values of x, y = 4. 1 • x + 0 • y = –3 Write in standard form. For all values of y, x = –3. 6-3

  13. y y 5 5 x x -5 -5 5 5 -5 -5 Example 3, page 299Graph each equation. • a) y = -3 b) x = 2

  14. y y 5 5 x x -5 -5 5 5 -5 -5 Example 3, page 299Graph each equation. • a) y = 5 b) y = 0

  15. y y 5 5 x x -5 -5 5 5 -5 -5 Example 3, page 299Graph each equation. • c) x = -4 d) x = 0

  16. Summary • What did you learn today?

  17. SUMMARY • Standard form of an equation is Ax + By = C • A horizontal line has equation y = #. • A vertical line has equation x = #.

  18. ASSIGNMENT Lesson 6-3 page 301 #1-26 all, 70-78 all

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