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

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

Graphing Linear Inequalities slope and y-intercept Jeff Bivin -- LZHS

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

y = 2x + 1 y ≤ 2x + 1 Shade TRUE 1 ≤ 2(2) + 1 1 ≤ 4 + 1 1 ≤ 5 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

y = 2x + 1 y ≤ 2x + 1 Don't Shade Shade FALSE 3 ≤ 2(-2) + 1 3 ≤ -4 + 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 other half-plane opposite the point. Jeff Bivin -- LZHS

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

y ≥ -3x + 2 y = -3x + 2 Shade Don't Shade FALSE 0 ≥ -3(0) + 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

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

Shade TRUE Now for the shading Let’s try (0, 0) 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

Graphing Linear Inequalities x- and y- intercepts Jeff Bivin -- LZHS

2x + 3y ≥ 5 find the x value when y = 0 find the y value when x = 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

2x + 3y ≥ 5 Shade TRUE Now for the shading Let’s try (4, 2) 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

2x + 3y ≥ 5 Shade Don't Shade FALSE 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

4x - y > 6 find the x value when y = 0 find the y value when x = 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

4x - y > 6 Don't Shade Shade FALSE 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

4x + 2y < 3 find the x value when y = 0 find the y value when x = 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

4x + 2y < 3 Shade TRUE Now for the shading Let’s try (0, 0) 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

3x - 2y < 7 find the x value when y = 0 find the y value when x = 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

3x - 2y < 7 Shade TRUE Now for the shading Let’s try (0, 0) 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