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Graphing Linear Inequalities

This tutorial explains how to graph linear inequalities, find slope and y-intercept, and determine x- and y-intercepts. It includes examples and step-by-step instructions.

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Graphing Linear Inequalities

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  1. Graphing Linear Inequalities slope & y-intercept & x- & y- intercepts Jeffrey Bivin Lake Zurich High School Jeff.bivin@lz95.org Last Updated: October 11, 2005

  2. Graphing Linear Inequalities • Select the desired MENU option below • Slope and y-intercept • x- & y- intercepts Jeff Bivin -- LZHS

  3. Graphing LinearInequalities slope and y-intercept Jeff Bivin -- LZHS

  4. y = 2x + 1 y ≤2x + 1 Run 1 y-intercept Rise b = 1 2 slope m = 2 Jeff Bivin -- LZHS

  5. y = 2x + 1 y ≤2x + 1 Now for the shading Pick a point on either side of the graph Let’s try (2, 1) Does the point satisfy the inequality? Shade 1 ≤2(2) + 1 1 ≤4 + 1 TRUE 1 ≤5 Therefore, shade the half-plane with the point. Jeff Bivin -- LZHS

  6. y = 2x + 1 y ≤2x + 1 What if we picked a point on the other side of the line? Don't Shade Let’s try (-2, 3) Does the point satisfy the inequality? Shade 3 ≤2(-2) + 1 3 ≤ -4 + 1 3 ≤-3 FALSE Therefore, shade the otherhalf-plane opposite the point. Jeff Bivin -- LZHS

  7. y = -3x + 2 y ≥-3x + 2 Run 1 y-intercept Rise b = 2 -3 slope m = -3 Jeff Bivin -- LZHS

  8. y = -3x + 2 y ≥-3x + 2 Now for the shading Pick a point on either side of the graph Let’s try (0, 0) Shade Does the point satisfy the inequality? Don't Shade 0 ≥-3(0) + 2 0 ≥0 + 2 FALSE 0 ≥2 Therefore, shade the other half-plane opposite the point. Jeff Bivin -- LZHS

  9. Run 3 y-intercept b = -1 Rise 2 slope Jeff Bivin -- LZHS

  10. Now for the shading Pick a point on either side of the graph Let’s try (0, 0) Shade Does the point satisfy the inequality? TRUE Therefore, shade the half-plane with the point. Jeff Bivin -- LZHS

  11. Graphing LinearInequalities x- and y- intercepts Jeff Bivin -- LZHS

  12. 2x + 3y ≥ 5 find the x value when y = 0 x-intercept 2x + 3(0)= 5 2x + 0= 5 2x= 5 find the y value when x = 0 y-intercept 2(0) + 3y= 5 0 + 3y= 5 3y= 5 Jeff Bivin -- LZHS

  13. 2x + 3y ≥ 5 Now for the shading Pick a point on either side of the graph Let’s try (4, 2) Shade Does the point satisfy the inequality? TRUE Therefore, shade the half-plane with the point. Jeff Bivin -- LZHS

  14. 2x + 3y ≥ 5 What if we picked a point on the other side of the line? Let’s try (-3, -4) Shade Does the point satisfy the inequality? Don't Shade FALSE Therefore, shade the other half-plane opposite the point. Jeff Bivin -- LZHS

  15. 4x - y > 6 find the x value when y = 0 x-intercept 4x - (0)= 6 4x - 0= 5 4x= 6 find the y value when x = 0 y-intercept 4(0) - y= 6 0 - y= 6 -y= 6 Jeff Bivin -- LZHS

  16. 4x - y > 6 Now for the shading Pick a point on either side of the graph Let’s try (0, 0) Does the point satisfy the inequality? Don't Shade Shade FALSE Therefore, shade the other half-plane opposite the point. Jeff Bivin -- LZHS

  17. 4x + 2y < 3 find the x value when y = 0 x-intercept 4x + 2(0)= 3 4x + 0= 3 4x= 3 find the y value when x = 0 y-intercept 4(0) + 2y= 3 0 + 2y= 3 2y= 3 Jeff Bivin -- LZHS

  18. 4x + 2y < 3 Now for the shading Pick a point on either side of the graph Let’s try (0, 0) Does the point satisfy the inequality? Shade TRUE Therefore, shade the half-plane with the point. Jeff Bivin -- LZHS

  19. 3x - 2y < 7 find the x value when y = 0 x-intercept 3x - 2(0)= 7 3x - 0= 7 3x= 7 find the y value when x = 0 y-intercept 3(0) - 2y= 7 0 - 2y= 7 -2y= 7 Jeff Bivin -- LZHS

  20. 3x - 2y < 7 Now for the shading Pick a point on either side of the graph Let’s try (0, 0) Does the point satisfy the inequality? Shade TRUE Therefore, shade the half-plane with the point. Jeff Bivin -- LZHS

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