9.5 Inequalities and two variables

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Presentation transcript:

9.5 Inequalities and two variables Goal(s): To determine whether a given ordered pair is a solution of an inequality To graph inequalities in 2 variables

Is (2,3) a solution of 5x + 2y < 23 ? 5(2) + 2(3) < 23 YES!

Is (2,1) a solution of x + y < 4 ? (2) + (1) < 4 YES!

Is (4,8) a solution of y > 2x + 1 ? (8) > 2(4) + 1 no

Is (-3,5) a solution of y > 2x + 1 ? (5) > 2(-3) + 1 yes Is (-3,6) a solution of y > 2x + 1 ? Is (-3,19) a solution of y > 2x + 1 ? Is (-3,458) a solution of y > 2x + 1 ?

Graph: 2x + 3y = 12 x y 4 6

To Graph an Inequality Use either the table method, x and y intercepts method, or slope intercept method to graph (graph as if it was an =) If it is a < or> the line will be a broken line and if it is a ≤ or ≥ the line will be solid Pick an ordered pair that is not on the line Plug the order pair into the inequality - if it makes the inequality true shade in everything on that same side of the line -if it makes the inequality false shade in everything on the opposite side of the line of the point

boundary line half-planes Graph: 2x + 3y  12 Is (1,1) a solution?

To graph: 2x – 5y < 10 Graph the boundary line 2x – 5y = 10. Use a dotted line for “< “ and a solid line for “”. Determine which half-plane is the solution by testing one point not on the boundary line. (0,0)

Graph: y – 2x  0 Graph the boundary line y – 2x = 10. Use a dotted line for “< “ and a solid line for “”. Determine which half-plane is the solution by testing one point not on the boundary line. (0,0) y = 2x + 0

Graph: x < 3

To Identify the Inequality Identify the y-intercept (that is your b) Count out the slope (rise over run from left to right) Look for solid or dashed line Plug in an ordered pair from the shaded area into your choices and see which inequality is true

This graph represents which inequality? Check (0,0) Check “b” Check slope + or neg

This graph represents which inequality? Check (0,0) Check x and y intercepts Check dotted line

Assignment Page 419 (2-40) even take graph paper

Graph on white boards X>3y Y< x-5 X+ Y ≥3 5X + 4Y ≤20