Linear Inequalities in Two Variables

Key Questions

  • How many solutions does a linear inequality in two variables have?

    The solution set of a single linear inequality is always a half-plane, so there are infinitely many solutions.

    I hope that this was helpful.

    Wataru · 15 · Oct 29 2014
  • How do you know if you need to shade above or below the line?

    Answer:

    The direction of the inequality will tell you this information.

    Explanation:

    Example: y >= 2x+3

    You would draw the line y = 2x+3 and shade above the line, since y is also greater than 2x+3.

    graph{y>=2x+3 [-10, 10, -5, 5]}

    Example: y < 1/2x-2

    You would draw the line y=1/2x-2 as a dashed line, then shade below the line since y is less than 1/2x-2.

    graph{y<1/2x-2 [-10, 10, -5, 5]}

    NJ · 6 · Mar 20 2018
  • How do you graph linear inequalities in two variables?

    The best way (when possible!) is to express the inequality bringing all the terms involing a variable on the left, and all the terms involving the other variable on the right. In the end, you'll have an inequality of the form y\le f(x) (or y\ge f(x)), and this is easy to graph, because if you can draw the graph of f(x), then you'll have that y\le f(x) represents all the area under the function f, and y\ge f(x), of course, the area over the function.

    For example, consider the inequality
    yx^2<-y+3x
    In this form, it would be very hard to say which points satisfy the inequality, but with some manipulations we obtain
    yx^2+y<3x
    y(x^2+1)<3x
    y<\frac{3x}{x^2+1}

    Now, the graph of \frac{3x}{x^2+1} is easy to draw, and the inequality is solved considering all the area below the graph, as showed:

    graph{y<3x/{x^2+1} [-10, 10, -5, 5]}

    Note that if you have y<f(x) the graph of the function f is not included, since it represents the points for which y=f(x).

    KillerBunny · 1 · Feb 1 2015

Questions

Linear Inequalities and Absolute Value