`x+y<=4`  graph the inequalitiesShow work

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embizze | High School Teacher | (Level 2) Educator Emeritus

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Graph `x+y<=4` :

The way to graph a linear inequality is to graph the line (solid if the inequality is inclusive like `<=,>=` , dotted if the inequality is exclusive like < or >). Then you pick a test point that is not on the line. If the point satisfies the inequality, every point on the same side of theline also satisfies the inequality.

(1) The line will be solid

(2) Graph the line `x+y=4` . There are various ways to do this; in slope-intercept form this is the line y=-x+4 so the y-intercept is 4 and the slope is -1, thus another point on the line is (1,3).

The line is given in standard form, so you could find the intercepts (0,4) and (4,0).

Or you could choose convenient x values and solve for y.

Regardless of your methods you get the line:

(3) Now choose a test point that is not on the line. If possible, I suggest choosing (0,0). Replacing x and y with 0 the inequality is `0+0<=4` which is true. Thus every point on the same side of the line ("underneath" the line) is a solution, so you should shade that side of the line.

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