Linear inequality represented by the graph is
[tex]\displaystyle y\leq \frac{1}{3}x-4[/tex]
Further explanation
Straight-line equations are mathematical equations that are described in the plane of cartesian coordinates
General formula
[tex]\large{\boxed{\bold{y-y1=m(x-x1)}}[/tex]
or
y = mx + c
Where
m = straight-line gradient which is the slope of the line
x1, y1 = the Cartesian coordinate that is crossed by the line
c = constant
The formula for a gradient (m) between 2 points
[tex]\large{\boxed{\bold{m= \frac{y2-y1}{x2-x1}}}[/tex]
If the intersection of the x-axis (b, 0) and the y-axis (0, a) then the equation of the line:
ax + by = ab
It says inequality if there are symbol forms like <,>,≤ or ≥
- Whereas linear inequality can have forms: ax + by> c
ax + by ≥ c
ax + by <c
ax + by ≤ c
In graphical form, line inequality can be
- dashed line because y does not include equals to
- a solid line because y includes equal to
For line inequality (positive coefficient y)
ax + by ≥ c then the solution is shaded upwards
ax + by ≤ c then the solution is shaded down
Or we input the values x, y from the point in the shaded area and put in the inequality line
From the picture we can determine the equation of the line
Line through 2 points (0, -4) and (-3, -5)
the gradient: [tex]\displaystyle =\frac{-5+4}{-3-0}\\\\=\frac{1}{3}[/tex]
the equation of the line:
[tex]\displaystyle y-y1=m(x-x1)\\\\y+4=\frac{1}{3}(x-0)\\\\=\frac{1}{3}x-4[/tex]
We check the point in the area of shading, for example (0, -6)
we input in the equation :
[tex]\displaystyle -6=\frac{1}{3}.0-4\\\\-6=-4[/tex]
Because -6 < -4 and the graph is solid line so the inequality line will be
[tex]\displaystyle y\leq \frac{1}{3}x-4[/tex]
Learn more
F (x) = x2 + 1 g (x) = 5 - x
htps: //brainly.com/question/2723982
the inverse of the function f (x) = 2x-10
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domain of the function
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Keywords: linear inequality,graph
