Answer:
y ≤ 3x − 1, y ≤ −x + 4
Step-by-step explanation:
The line f(x) is solid and goes through the points (0, 4) and (4, 0) and is shaded below the line.
The line that satisfies the point (0,4) and (4,0) is y=-x+4
Since it is shaded below the line, we have the inequality sign: [tex]\leq[/tex]
Therefore, one of the lines is: [tex]y\leq -x+4[/tex]
The line g(x) is solid and goes through the points (0, -1) and (2, 5) and is shaded below the line.
Slope, [tex]m=\frac{5-(-1)}{2-0}=3[/tex]
When x=0, y=-1
y=mx+b
y=3x+b
-1=3(0)+b
b=-1
Therefore, the equation of the line is: [tex]y=3x-1[/tex]
Since it is shaded below the line, we have the inequality sign: [tex]\leq[/tex]
Therefore, the other line is: [tex]y\leq 3x-1[/tex]
An inequality is a comparison between two expressions not based on equality
The graph represents the system of the inequalities; y ≤ 3·x - 1, y ≤ -x + 4
Reason:
The given parameters are;
Points on the line f(x) = (0, 4), (4, 0)
[tex]Slope \ of \ the \ line, \ m =\dfrac{4-0}{0-4} = -1[/tex]
Therefore;
The equation of the line is y - 0 = -1·(x - 4), which gives;
y = -x + 4
The inequality representing the line is y ≤ -x + 4
Points on the line g(x) = (0, -1), (2, 5)
[tex]Slope \ of \ the \ line, \ m =\dfrac{-1-5}{0-2} = \dfrac{-6}{-3} =3[/tex]
Equation of the line is y - (-1) = 3·(x - 0)
∴ y = 3·x - 1
The inequality is y ≤ 3·x - 1,
The graph which represent the system of inequalities are;
y ≤ 3·x - 1, y ≤ -x + 4
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