How To Solve An Equation In Standard Form

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1 Lesson 9: Graphing Standard Form Equations Lesson 2 of 2 Method 2: Rewriting the equation in slope intercept form Use the same strategies that were used for solving equations: Your goal is to solve for. Example 1 Graph the following equations: 6x 8y = -16 x y = -9

2 Lesson 9: Graphing an Equation in Standard Form (2 of 2) Directions: First rewrite each equation in slope intercept form. Then identify the slope and y- intercept. Last, graph your equation on the grid x y = x 3y = 6 Slope = y-intercept = Slope = y-intercept =

3 3. -4x y = x +9y = -9 Slope = y-intercept = Slope = y-intercept =

4 5. Which one of the following equations shows 12x 3y = 6 in slope intercept form? A. 3y = 12x -6 B. y = 4x -2 C. y = -4x + 2 D. y = 4x Write an equation (in slope intercept form) that is equivalent to: 8x -2y = Which one of the following equations shows -3y = 6 12x in slope intercept form? A. -3y = 6 12x B. y = 6 12x C. y = 4x 2 D. y = -4x Given the following equation: 3x 5y = 10, identify the slope of the line.

5 9. Given the following equation: 3x 8y = 16, identify the slope and y-intercept of the line. 10. Are the following equations equivalent? Justify your answer. 2x 4y = 8 & y = -1/2x Write an equation in slope intercept form that is equivalent to: 2x 5y = 12 (2 points) 2. Given the equation: 4x + 3y = 8. Identify the slope and y-intercept of the line. (2 points) 3. Are the following equations equivalent? Explain your answer, then justify by graphing each line on the grid below. (4 points) 2x 3y = 15 4x = 6y + 36

6 Lesson 9: Graphing an Equation in Standard Form Answer Key Directions: For each problem below, identify the slope and the y-intercept. 1. 3x +2y = x 3y = 6 3x 3x +2y = -4 3x Subtract 3x -2x +2x 3y = 6 +2x Add 2x 2y = -4 3x Divide by y = 6 +2x Divide by y = -2-3x y = -2 2/3x 2 y = -2/3x 2 Switch terms around y = -3/2x -2 Switch terms around Slope = -2/3 y-intercept = -2 Slope = -3/2 y-intercept = -2

7 3. -4x y = x +9y = -9-4x +4x y = -2 +4x Add 4x -3x +3x +9y = -9 +3x Add 3x -y = -2 +4x Divide by y = x Divide by y = 2 4x y = /3x y = -4x +2 Switch terms around y = 1/3 x 1 Switch terms around Slope = -4 y-intercept = 2 Slope = 1/3 y-intercept = -1

8 5. Which one of the following equations shows 12x 3y = 6 in slope intercept form? A. 3y = 12x -6 B. y = 4x -2 C. y = -4x + 2 D. y = 4x +2 You can eliminate A and C immediately because slope intercept form must by y =. The y cannot have a coefficient, nor can it be negative. Eliminating answers that do not make sense is a great test taking strategy! 12x 3y = 6 12x -12x -3y = 6 12x -3y = -12x y = 4x -2 - The answer is B 6. Write an equation (in slope intercept form) that is equivalent to: 8x -2y = 12 8x -8x 2y = 12-8x Subtract 8x from both sides -2y = -8x + 12 & reverse the terms on the right hand side. -2y = -8x + 12 Divide all terms by y = 4x 6 The equation written in slope intercept form. 7. Which one of the following equations shows -3y = 6 12x in slope intercept form? A. -3y = 6 12x B. y = 6 12x C. y = 4x 2 You can eliminate letter A, because slope intercept form must be solved for y. This equation is almost in slope intercept form. We must get y by itself on the left hand side; therefore, we need to get rid of the coefficient of y = 6 12x Divide all terms by D. y = -4x + 2 y = x OR y = 4x 2 Equation written in slope intercept form. 8. Given the following equation: 3x 5y = 10, identify the slope of the line. In order to find the slope, we must rewrite the equation in slope intercept form. 3x -3x -5y = 10-3x Subtract 3x from both sides -5y = -3x + 10 & reverse the terms on the right hand side. -5y = -3x + 10 Divide all terms by y = 3/5x - 2 Equation written in slope intercept form. Copyright The slope 2009 of the Algebra-class.com line is 3/5. (3/5 is the coefficient of x, therefore, it is the slope)

9 9. Given the following equation: 3x 8y = 16, identify the slope and y-intercept of the line. 3x -3x 8y = 16 3x Subtract 3x from both sides. -8y = -3x + 16 & reverse the terms on the right hand side. -8y = -3x + 16 Divide all terms by y = 3/8x 2 Equation written in slope intercept form. The slope of the line is 3/8 and the y-intercept is Are the following equations equivalent? Justify your answer. 2x 4y = 8 & y = -1/2x -2 In order to determine if the equations are equivalent, you must rewrite the standard form in slope intercept form. If the equations are equivalent, then they will be the exact same equation when written in slope intercept form. Let s rewrite the standard form equation in slope intercept form. 2x 4y = 8 2x -2x 4y = 8-2x Subtract 2x from both sides. -4y = -2x + 8 & reverse the terms on the right hand side. -4y = -2x + 8 Divide all terms by y = 1/2x - 2 Equation written in slope intercept form. The equations are not equivalent. y = 1/2x -2 & y = -1/2x 2 differ because equation #1 has a positive slope and equation #2 has a negative slope.

10 1. Write an equation in slope intercept form that is equivalent to: 2x 5y = 12 (2 points) In order to write the equation in slope intercept form, I must solve for y. 2x 5y = 12 2x 2x 5y = 12 2x Original equation Subtract 2x from both sides -5y = -2x + 12 and rewrite in correct format -5y/-5 = -2x/ /-5 Divide ALL terms by -5 y = 2/5x 12/5 The equation in slope intercept form is: y = 2/5x 12/5 2. Given the equation: 4x + 3y = 8. Identify the slope and y-intercept of the line. (2 points) In order to identify the slope and y-intercept of the line, we must rewrite the equation in slope intercept form. Therefore, we must solve for y. 4x + 3y = 8 4x 4x + 3y = 8 4x 3y = -4x + 8 Original equation Subtract 4x from both sides and rewrite in correct format 3y/3 = -4x/3 + 8/3 Divide ALL terms by 3 y = -4/3x + 8/3 The equation in slope intercept form is: y = -4/3x + 8/3. Therefore, the slope is -4/3 and the y- intercept is 8/3.

11 3. Are the following equations equivalent? Explain your answer, then justify by graphing each line on the grid below. (4 points) 2x 3y = 15 4x = 6y + 36 We can tell if the equations are equivalent by rewriting both in slope intercept form: 2x 3y = 15 2x-2x 3y = 15 2x Original equation Subtract 2x from both sides -3y = -2x y/-3 = -2x/ /-3 Divide All terms by -3 y = 2/3x 5 Equation in slope intercept form 4x = 6y +36 4x 36= 6y x 36 = 6y Original equation Subtract 36 from both sides 4x/6 36/6 = 6y/6 Divide All terms by 6 2/3x 6 = y Equation in slope intercept form y = 2/3x - 6 These equations are not equivalent because when written in slope intercept form, they are not the same exact equation. The graph shows parallel lines, which means that the equations are not equivalent. They have the same slope but different y-intercepts and this is why they are parallel.

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