How to write a system of linear inequalities from a graph
How to write an inequality from a graph
A linear inequality on the plane can have one of the following forms: Notice that all of these linear inequalities have linear equations, which can be associated with them if we replace the inequality with an equality. Well, that's going to be 30 grams of sugar per muffin. We can use the method described above to find each linear inequality associated with the boundary lines for this region. This line will tell us-- well, let's take this point so we get to an integer. That is the inequality that is depicted in this graph, where this is just the line, but we want all of the area above and equal to the line. Its y-intercept is right there at y is equal to negative 2. So plus 30 grams of sugar per muffin times the number of muffins. Well, we're told right over here she requires 35 grams of sugar per cupcake. So this has to be greater than or equal. In addition, the half-plane involves a shaded portion of the plane either above or below the boundary line or to the left or right of a vertical boundary line. So if I went back 4, if delta x was negative 4, if delta x is equal to negative 4, then delta y is equal to positive 2. In this example, we can use the origin 0, 0 as a test point.
She needs to use up, "Shawna needs to use up at least grams of sugar "to make cupcakes and muffins, "and she wants to use at most grams of flour. Modeling with linear inequalities Video transcript - [Voiceover] So we're told a cupcake requires 35 grams of sugar and 50 grams of flour.
Solving systems of linear inequalities worksheet answers
Use the test point to determine which half-plane should be shaded. That is the inequality that is depicted in this graph, where this is just the line, but we want all of the area above and equal to the line. And just to reinforce, you could have done this anywhere. Recall that a system of linear inequalities is a set of linear inequalities in the same variables. Finally, our graph should include the points x, y which satisfy the inequality We can determine these points by taking a point on one side of the line and testing its coordinates in our inequality. Let's say x is equal to 1. And then for the muffins, she uses 65 grams of flour per muffin times the number of muffins.
If the inequality is of the form then the region below the line is shaded and the boundary line is solid. Notice that it is not true that and so we shade the half-plane that does not include the origin.
So plus 30 grams of sugar per muffin times the number of muffins. I just want to reinforce that it's not dependent on how far I move along in x or whether I go forward or backward.
How to write a linear inequality
Recall that a system of linear inequalities is a set of linear inequalities in the same variables. So this is the total sugar from the cupcakes. We can just set up the inequality that represents the condition based on the number of grams of sugar which is this condition right over here. So no more than grams. So first we just have to figure out the equation of this line. In this case, our system is: Tutorial Details 20 Minutes Pre-requisite Concepts Students should be able to write the equation of a line from its graph and vice versa graph a line from its equation , and define and graph a system of linear inequalities. Modeling with linear inequalities Video transcript - [Voiceover] So we're told a cupcake requires 35 grams of sugar and 50 grams of flour. Well, that's going to be 30 grams of sugar per muffin. Use the test point to determine which half-plane should be shaded. So 50 grams per cupcake times the number of cupcakes. We can figure out its y-intercept just by looking at it. I know that, because they shaded in this whole area up here.
That's the equation of this line right there. That's how much flour she's going to use for the cupcakes.
Our change in y is equal to negative 1.
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