Graphing a Linear Inequality Graphing a linear inequality

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Graphing a Linear Inequality Graphing a linear inequality is very similar to graphing a

Graphing a Linear Inequality Graphing a linear inequality is very similar to graphing a linear equation.

Graphing Linear Inequalities slope & y-intercept & x- & y- intercepts

Graphing Linear Inequalities slope & y-intercept & x- & y- intercepts

Graphing Linear Inequalities Select the desired MENU option below 1. Slope and y-intercept 2.

Graphing Linear Inequalities Select the desired MENU option below 1. Slope and y-intercept 2. x- & y- intercepts

Graphing Linear Inequalities

Graphing Linear Inequalities

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

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

y= ≤ 2 x + 1 Now for the shading Pick a point on

y= ≤ 2 x + 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? 1 ≤ 2(2) + 1 1≤ 4+1 1≤ 5 Therefore, shade the half-plane with the point.

y= ≤ 2 x + 1 What if we picked a point on the

y= ≤ 2 x + 1 What if we picked a point on the other side of the line? Let’s try (-2, 3) Does the point satisfy the inequality? 3 ≤ 2(-2) + 1 3 ≤ -4 + 1 3 ≤ -3 Therefore, shade the other half-plane opposite the point.

y= ≥ -3 x + 2 y-intercept b=2 slope m = -3 Run 1

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

y= ≥ -3 x + 2 Now for the shading Pick a point on

y= ≥ -3 x + 2 Now for the shading Pick a point on either side of the graph Let’s try (0, 0) Does the point satisfy the inequality? 0 ≥ -3(0) + 2 0≥ 0+2 0≥ 2 Therefore, shade the other half-plane opposite the point.

Run 3 y-intercept b = -1 slope Rise 2

Run 3 y-intercept b = -1 slope Rise 2

Now for the shading Pick a point on either side of the graph Let’s

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

Graphing Linear Inequalities

Graphing Linear Inequalities

2 x + 3 y ≥ 5 x-intercept 2 x + 3(0) = 5

2 x + 3 y ≥ 5 x-intercept 2 x + 3(0) = 5 2 x + 0 = 5 2 x = 5 y-intercept 2(0) + 3 y = 5 0 + 3 y = 5

2 x + 3 y ≥ 5 Now for the shading Pick a point

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

2 x + 3 y ≥ 5 What if we picked a point on

2 x + 3 y ≥ 5 What if we picked a point on the other side of the line? Let’s try (-3, -4) Does the point satisfy the inequality? Therefore, shade the other half-plane opposite the point.

4 x - y > 6 x-intercept 4 x - (0) = 6 4

4 x - y > 6 x-intercept 4 x - (0) = 6 4 x - 0 = 5 4 x = 6 y-intercept 4(0) - y = 6 0 -y=6 -y = 6

4 x - y > 6 Now for the shading Pick a point on

4 x - 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? Therefore, shade the other half-plane opposite the point.

4 x + 2 y < 3 x-intercept 4 x + 2(0) = 3

4 x + 2 y < 3 x-intercept 4 x + 2(0) = 3 4 x + 0 = 3 4 x = 3 y-intercept 4(0) + 2 y = 3 0 + 2 y = 3

4 x + 2 y < 3 Now for the shading Pick a point

4 x + 2 y < 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? Therefore, shade the half-plane with the point.

3 x - 2 y < 7 x-intercept 3 x - 2(0) = 7

3 x - 2 y < 7 x-intercept 3 x - 2(0) = 7 3 x - 0 = 7 3 x = 7 y-intercept 3(0) - 2 y = 7 0 - 2 y = 7 -2 y = 7

3 x - 2 y < 7 Now for the shading Pick a point

3 x - 2 y < 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? Therefore, shade the half-plane with the point.