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3-4 Equations of Lines.ppt

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This document contains information about different forms of linear equations: slope-intercept form, point-slope form, and a method for finding an equation given two points on a line. It defines each form, provides examples of equations written in the different forms, and includes a set of practice problems with answers for finding equations of lines given characteristics like slope, intercepts, and points on the line.

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SEC 3-4 JIM SMITH JCHS 3108.1.2 Determine position using coordinate systems 3108.1.12 Historical development of geometry
SLOPE INTERCEPT FORM THE EQUATION ON A LINE CAN BE WRITTEN IF WE KNOW THE SLOPE OF THE LINE AND THE Y-INTERCEPT. FROM ALGEBRA WE KNOW THIS FORM IS y = mx + b WHERE M IS THE SLOPE OF THE LINE AND B IS THE Y-INTERCEPT. IF OUR SLOPE = 4 AND THE Y-INTERCEPT IS 3, THEN y = 4x + 3 . THE KEY IS HAVING THE Y ON ONE SIDE BY ITSELF. SLOPE Y-INTERCEPT EQUATION 2 8 1 -3 0 6 4 0 y = 2x + 8 y = x 3 y = 6 y = 4x EQUATION SLOPE Y-INTERCEPT Y = 7x 2 Y = 4x + 5 2Y + 3X = 8 7 -2 4 5 -3 4 2
POINT SLOPE FORM IF WERE GIVEN THE SLOPE OF A LINE AND A POINT ON THAT LINE OTHER THAN THE Y INTERCEPT, THEN WE USE THE POINT SLOPE FORM y - y = m ( x - x ) WHERE ( x, y ) ARE THE COORDINATES OF THE POINT ON THE LINE AND m IS THE SLOPE. SLOPE = 2 LINE PASSES THROUGH ( 3 , 5 ) y 5 = 2 ( x 3 ) POINT SLOPE FORM y 5 = 2x 6 y = 2x - 1 SLOPE INTERCEPT FORM YOU CAN FIND THE Y-INTERCEPT BY SOLVING FOR (b) Y = mx + b 5 = 2(3) + b 5 = 6 + b B = -1 y = 2x - 1
2 POINTS, NO SLOPE IF WE HAPPEN TO KNOW 2 POINTS ON A LINE BUT NOT THE SLOPE, WE NEED TO FIND THE SLOPE FIRST. A LINE PASSES THROUGH ( 2 , 8 ) AND ( 3 , 10 ) FIND THE SLOPE FIRST 10 8 3 2 M = 2 USE EITHER ONE OF THE POINTS AND PLUG IN POINT SLOPE FORM Y 8 = 2 ( x 2 ) Y 8 = 2x 4 Y = 2x + 4 OR 10 8 = m ( 3 2 ) 2 = m Then use point slope form
1. Which is an equation of the line in the graph shown? A. y = 2x 3 C. y = -2x + 3 B. y = 2x + 3 D. y = -2x - 3 2. Which is an equation of the line with slope 0 and passing through the point at (-2, 3)? A. y = 3 C. y = 0 B. x = -2 D. y = -2x + 3 3. Which is an equation of the line with slope = 3, and y-intercept = -1 . A. y = -x + 3 C. y = 3x - 1 B. y = x - 3 D. y = -3x + 1 4. Write the equation of the line perpendicular to y = 遜 x + 6 that passes through the point (3,-13) A. y = 1/2x - 6 C. y = 2x + 6 B. y = -2x - 7 D. y = -2x + 7 5. Write the equation of the line that has an x-intercept of 6 and a y-intercept of 3. A. y = 3x + 5 C. y = 1/2x - 3 B. y = -2x + 3 D. y = 1/2x + 3 From glencoe.com A. A. C. B. D.

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3-4 Equations of Lines.ppt

  • 1. SEC 3-4 JIM SMITH JCHS 3108.1.2 Determine position using coordinate systems 3108.1.12 Historical development of geometry
  • 2. SLOPE INTERCEPT FORM THE EQUATION ON A LINE CAN BE WRITTEN IF WE KNOW THE SLOPE OF THE LINE AND THE Y-INTERCEPT. FROM ALGEBRA WE KNOW THIS FORM IS y = mx + b WHERE M IS THE SLOPE OF THE LINE AND B IS THE Y-INTERCEPT. IF OUR SLOPE = 4 AND THE Y-INTERCEPT IS 3, THEN y = 4x + 3 . THE KEY IS HAVING THE Y ON ONE SIDE BY ITSELF. SLOPE Y-INTERCEPT EQUATION 2 8 1 -3 0 6 4 0 y = 2x + 8 y = x 3 y = 6 y = 4x EQUATION SLOPE Y-INTERCEPT Y = 7x 2 Y = 4x + 5 2Y + 3X = 8 7 -2 4 5 -3 4 2
  • 3. POINT SLOPE FORM IF WERE GIVEN THE SLOPE OF A LINE AND A POINT ON THAT LINE OTHER THAN THE Y INTERCEPT, THEN WE USE THE POINT SLOPE FORM y - y = m ( x - x ) WHERE ( x, y ) ARE THE COORDINATES OF THE POINT ON THE LINE AND m IS THE SLOPE. SLOPE = 2 LINE PASSES THROUGH ( 3 , 5 ) y 5 = 2 ( x 3 ) POINT SLOPE FORM y 5 = 2x 6 y = 2x - 1 SLOPE INTERCEPT FORM YOU CAN FIND THE Y-INTERCEPT BY SOLVING FOR (b) Y = mx + b 5 = 2(3) + b 5 = 6 + b B = -1 y = 2x - 1
  • 4. 2 POINTS, NO SLOPE IF WE HAPPEN TO KNOW 2 POINTS ON A LINE BUT NOT THE SLOPE, WE NEED TO FIND THE SLOPE FIRST. A LINE PASSES THROUGH ( 2 , 8 ) AND ( 3 , 10 ) FIND THE SLOPE FIRST 10 8 3 2 M = 2 USE EITHER ONE OF THE POINTS AND PLUG IN POINT SLOPE FORM Y 8 = 2 ( x 2 ) Y 8 = 2x 4 Y = 2x + 4 OR 10 8 = m ( 3 2 ) 2 = m Then use point slope form
  • 5. 1. Which is an equation of the line in the graph shown? A. y = 2x 3 C. y = -2x + 3 B. y = 2x + 3 D. y = -2x - 3 2. Which is an equation of the line with slope 0 and passing through the point at (-2, 3)? A. y = 3 C. y = 0 B. x = -2 D. y = -2x + 3 3. Which is an equation of the line with slope = 3, and y-intercept = -1 . A. y = -x + 3 C. y = 3x - 1 B. y = x - 3 D. y = -3x + 1 4. Write the equation of the line perpendicular to y = 遜 x + 6 that passes through the point (3,-13) A. y = 1/2x - 6 C. y = 2x + 6 B. y = -2x - 7 D. y = -2x + 7 5. Write the equation of the line that has an x-intercept of 6 and a y-intercept of 3. A. y = 3x + 5 C. y = 1/2x - 3 B. y = -2x + 3 D. y = 1/2x + 3 From glencoe.com A. A. C. B. D.