Linear inequality represented by the graph is
[tex]\displaystyle (A)y\geq \dfrac{1}{3}x-1[/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-y_1=m(x-x_1)}}[/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=\dfrac{y_2-y_1}{x_2-x_1}}}[/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 (3,0) and (0,-1)
the gradient:
[tex]\displaystyle m=\frac{-1-0}{0-3}\\\\\displaystyle m=\frac{1}{3}[/tex]
the equation of the line: point (3,0)
[tex]\displaystyle y-0=\frac{1}{3}(x-3)\\\\\displaystyle y=\frac{1}{3}x-1[/tex]
We check the point in the area of shading, for example (0, 0)
we input in the equation :
[tex]\displaystyle 0=\frac{1}{3}.0-1\\\\0=-1[/tex]
Because 0 > -1 and the graph is solid line so the inequality line will be
[tex]\displaystyle (A)y\geq \dfrac{1}{3}x-1[/tex]
Learn more
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Keywords: linear inequality,graph
