`x+y<=4` graph the inequalities Show work
- print Print
- list Cite
Expert Answers
calendarEducator since 2011
write3,000 answers
starTop subjects are Math, Science, and Business
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.
Related Questions
- Solve the inequality `|1/2 x-3| lt= 4`
- 2 Educator Answers
- find the exact length of the curve, `x=(1/8)y^4+1/(4y^2)` `1<=y<=2` please explain as...
- 1 Educator Answer
- y<x-5 2x+4y>8 graph inequalities show all work shade
- 1 Educator Answer
- Which of the quadratic functions has the widest graph? A. y = (1/3)x^2 B. y = -4*x^2 C. y =...
- 2 Educator Answers
- graph the system of inequalities (shade each half-plane solution,not only the overall x<3...
- 1 Educator Answer
Unlock This Answer Now
Start your 48-hour free trial to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.