Answer:
Please find attachment for graph.
Explanation:
The graph of an inequality is a set of points that represents all solutions related to the inequality. The set of all point which followed both condition of inequality. The set of points are shown as double shaded area in the graph.
Further explanation:
In the graphing of a linear inequality the following 3 steps can be used.
1. Initially the given equation of inequality should be rearranged. After this rearrangement "y" should be on the left and everything else on the right. The final equation should be a y = function of x.
2. Then the "y=" line should be plotted. The line should be a solid line for y≤ or y≥, and a dashed line for y< or y>.
3. Then take a test point for each inequality check true or false.
- If true then shade towards the test point.
- If false then shade away from the test point.
In the given system of inequality of [tex]4x+y>1[/tex] and [tex]y\leq\dfrac{3}{2}x+2[/tex]
#For first equation, [tex]4x+y>1[/tex]
The rearranged equation is, y = 1 -4x
The slope of this graph is negative. The intercept should be +1.
As this is y > type a dashed line should be used to plot the graph.
Take test point: (0,0)
[tex]4\cdot 0+0>1[/tex]
[tex]0>1[/tex]
False, shade away from (0,0)
#For equation, [tex]y\leq\dfrac{3}{2}x+2[/tex]
The rearranged equation is,
[tex]y=\dfrac{3}{2}x+2[/tex]
The slope of this graph is positive.
The intercept should be +2. As this is y≤ type a solid line should be used to plot the graph.
Take test point (0,0)
[tex]0\leq\dfrac{3}{2}\cdot 0+2[/tex]
[tex]0\leq2[/tex]
True, shade towards (0,0)
Please find the attachment for graph.
Learn more:
1. Representation of inequalities: https://brainly.com/question/11220142 Answered by Sqdancefan
2. Graph the inequality: https://brainly.com/question/13334731, Answered by Pinquancaro
Keywords
Inequalities, dashed line, solid line, system of inequality, system of equation by graphing.
